What do you mean by Co-ordinates (Abscissa and Ordinate)? Explain with figure. -Maths 9th

1 Answer

Answer :

Co-ordinate Geometry is that branch of geometry in which two numbers, called co-ordinates are used to indicate the position of a point in a plane and which make use of algebraic methods in the study of geometric figures.

Related questions

Description : Draw the graph of the equation 3x + 4y = 12 and find the co-ordinates of the points of intersection of the equation with the co-ordinate axes. -Maths 9th

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Description : Signs of the abscissa and ordinate of a point in the second quadrant are respectively. -Maths 9th

Last Answer : (C) In second quadrant, X-axis is negative and Y-axis is positive. So, sign of abscissa of a point is negative and sign of ordinate of a point is positive.

Description : The points whose abscissa and ordinate have different signs will lie in -Maths 9th

Last Answer : (d) The points whose abscissa and ordinate have different signs will be of the form (-x, y) or (x, – y)and these points will lie in II and IV quadrants.

Description : Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa. -Maths 9th

Last Answer : Let the abscissa of the point be x, According to the question, Ordinate (y) = 3 x Abscissa ⇒ y=3x When x = 1, then y = 3 x 1 = 3 and when x = 2, then y = 3 x 2 = 6. Here, ... the line AB. Hence, y = 3x is the required equation such that each point on its graph has an ordinate 3 times its abscissa.

Description : Signs of the abscissa and ordinate of a point in the second quadrant are respectively. -Maths 9th

Last Answer : (C) In second quadrant, X-axis is negative and Y-axis is positive. So, sign of abscissa of a point is negative and sign of ordinate of a point is positive.

Description : The points whose abscissa and ordinate have different signs will lie in -Maths 9th

Last Answer : (d) The points whose abscissa and ordinate have different signs will be of the form (-x, y) or (x, – y)and these points will lie in II and IV quadrants.

Description : Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa. -Maths 9th

Last Answer : Let the abscissa of the point be x, According to the question, Ordinate (y) = 3 x Abscissa ⇒ y=3x When x = 1, then y = 3 x 1 = 3 and when x = 2, then y = 3 x 2 = 6. Here, ... the line AB. Hence, y = 3x is the required equation such that each point on its graph has an ordinate 3 times its abscissa.

Description : Express the given statement in the form of a linear equation in two variables. The sum of the ordinate and abscissa of a point is 6. -Maths 9th

Last Answer : Solution :- x+y = 6

Description : Determine the point on the graph of the linear equation x + y = 6, whose ordinate is 2 times its abscissa. -Maths 9th

Last Answer : Solution :-

Description : The point in which abscissa and ordinate have different signs will lie in which quadrant (s)? -Maths 9th

Last Answer : Solution :- II and IV quadrants.

Description : linear equation such that each point on its graph has an ordinate one more than 3×1÷2 times its abscissa -Maths 9th

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Description : The ordinate of a point is thrice its abscissa. Express the statement in the form of a linear equation in two variables. -Maths 9th

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Description : The product of the abscissa and the ordinate of a point P is negative. In which quadrants can the point lie ? -Maths 9th

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Description : The point whose abscissa is equal to its ordinate and which is equidistant from A(–1, 0) and B(0, 5) is -Maths 9th

Last Answer : Putting \(x\) = 0 in equation of one of the lines say 9\(x\) + 40y -20 = 0, we get y = \(rac{1}{2}\)∴ A point on 9\(x\) + 40y - 20 = 0 is \(\big(0,rac{1}{2}\big)\)∴ Distance of \(\big(0,rac{1}{2}\big) ... imesrac{1}{2}+21\big|}{\sqrt{9^2+40^2}}\) = \(rac{|41|}{\sqrt{1681}}\) = \(rac{41}{41}\) = 1.

Description : Without plotting the points indicate the quadrant in which they lie, if : (i) ordinate is 5 and abscissa is – 3 (ii) abscissa is -5 and ordinate is – 3 -Maths 9th

Last Answer : answer:

Description : Without plotting the points indicate the quadrant in which they will lie, if (i) the ordinate is 5 and abscissa is – 3 -Maths 9th

Last Answer : (i) In the point (−3,5) abscissa is negative and ordinate is positive, so it lies in the second quadrant. (ii) In the point (−5,−3) abscissa and ordinate both are negative, so it lies in the ... . (iv) In the point (3,5) abscissa and ordinate both are positive, so it lies in the first quadrant

Description : In the adjoining figure, P and Q have co-ordinates (4, 6)and (0, 3) respectively. Find (i) the co-ordinates of R (ii) Area of quadrilateral OAPQ. -Maths 9th

Last Answer : Let the line 2x + 3y - 30 = 0 divide the join of A(3, 4) and B(7, 8) at point C(p, q) in the ratio k : 1. Then,p = \(rac{7k+3}{k+1}\), q = \(rac{8k+4}{k+1}\)As the point C lies on the line 2x + 3y - 30 ... {3}{2}+1},rac{8 imesrac{3}{2}+4}{rac{3}{2}+1}\bigg)\) = \(\big(rac{27}{5},rac{32}{5}\big)\).

Description : Any convenient co-ordinate system or Cartesian co-ordinates which can be usedto define the picture is called a.spherical co-ordinates b.vector co-ordinates c.viewport co-ordinates d.world co-ordinates

Last Answer : d.world co-ordinates

Description : For a ternary mixture, in which equilateral triangular co-ordinate is used in leaching and extraction, a __________ of the equilateral triangular co-ordinates. (A) Binary mixture is ... Ternary mixture is represented by the sides (D) Pure component is represented by the apex

Last Answer : (D) Pure component is represented by the apex

Description : What do you mean by Co-ordinate Geometry? -Maths 9th

Last Answer : (a) \(rac{2^n}{5^n}\)In any number the last digits can 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Therefore, the last digit of each number can be chosen in 10 ways. ∴ Exhaustive number of ways = 10n. If the ... , favourable number of ways = 4n ∴ Required probability = \(rac{4^n}{10^n}\) = \(rac{2^n}{5^n}\).

Description : Distance Formula for co-ordinates: -Maths 9th

Last Answer : The position of each point of the plane is determined with reference to the rectangular axes by means of a pair of numbers called co-ordinates which are distances of the point from the respective axes. The distance of the ... are (x, 0) and the co-ordinates of any point of the y-axis are (0, y)

Description : Section formula for co-ordinates: -Maths 9th

Last Answer : The co-ordinate axes separate the plane into four regions called the quadrants. By custom the quadrants are numbered I, II, III, IV, in the counter clockwise direction as shown in the figure. (i) For distances along the x- ... +)X′OY′3rd quadrantx < 0, y < 0(-, -)XOY′4th quadrantx > 0, y < 0(+, -)

Description : Find the co-ordinates of the points on the x-axis which are at a distance of 10 units from the point (– 4, 8)? -Maths 9th

Last Answer : (a) Internal division: If P(x, y) divides the line segment formed by the joining of the points A (x1, y1) and B (x2, y2) internally in the ratio m1 : m2. Then\(x=rac{m_1x_2+m_2x_1}{m_1+m_2}\) and \(y=rac ... : 1, the co-ordinates of the mid-point are \(\bigg(rac{x_1+x_2}{2},rac{y_1+y_2}{2}\bigg)\).

Description : Find the co-ordinates of the circumcentre of the triangle whose vertices are (3, 0), (–1, –6) and (4, –1). Also find its circum-radius. -Maths 9th

Last Answer : Let A ≡ (2, - 2), B ≡ (-2, 1), C ≡ (5, 2 ). Then,AB = \(\sqrt{(-2-2)^2+(1+2)^2}\) = \(\sqrt{16+9}\) = \(\sqrt{25}\) = 5BC = \(\sqrt{(5+2)^2+(2-1)^2}\) = \(\sqrt{49+1}\) = \(\sqrt{50}\) = \( ... of ΔABC = \(rac{1}{2}\) x base x height = \(rac{1}{2}\) x AB x AC = \(rac{1}{2}\)x 5 x 5 = 12.5 sq. units.

Description : Let the opposite angular points of a square be (3, 4) and (1, – 1), Find the co-ordinates of the remaining angular points. -Maths 9th

Last Answer : P ≡ (-3, 2), Q ≡ (-5, -5), R ≡ (2, -3), S ≡ (4, 4)∴ PQ = \(\sqrt{(-5+3)^2+(-5-2)^2}\) = \(\sqrt{4+49}\) = \(\sqrt{53}\)QR = \(\sqrt{(2+5)^2+(-3+5)^2}\) = \(\sqrt{49+4}\) = \ ... of rhombus = \(rac{1}{2}\) x (Product of length of diagonals) = \(rac{1}{2}\) x \(5\sqrt2\) x \(9\sqrt2\) = 45 sq. units.

Description : The co-ordinates of mid-points of sides of a triangle are (1, 2), (0, –1) and (2, –1). Find its centroid. -Maths 9th

Last Answer : ABCD is a parallelogram, if the mid-points of diagonals AC and BD have the same co-ordinates (∵ Diagonals of a parallelogram bisect each other)Co-ordinates of mid-point of AC are \(\bigg(rac{a+2}{2},rac{-11+15}{2}\bigg)\) = \(\bigg(rac ... \(rac{a+2}{2}\) = 3 and 2 = \(rac{b+1}{2}\) ⇒ a = 4, b = 3.

Description : Find the co-ordinates of the in-centre of the triangle whose vertices are (–36, 7), (20, 7) and (0, –8). -Maths 9th

Last Answer : Let A(1, 2), B(0, -1) and C(2, -1) be the mid-points of the sides PQ, QR and RP of the triangle PQR. Let the co-ordinates of P, Q and R be (x1, y1), (x2, y2) and (x3 , y3) respectively. Then, by the mid- ... ordinates of centroid of ΔPQR = \(\bigg(rac{3+(-1)+1}{3},rac{2+2+(-4)}{3}\bigg)\) = (1, 0).

Description : (–2, –1) and (4, –5) are the co-ordinates of vertices B and D respectively of rhombus ABCD. Find the equation of the diagonal AC. -Maths 9th

Last Answer : 3\(x\) - 2y + 5 = 0 ⇒ -2y = -3\(x\) - 5 ⇒ y = \(rac{3}{2}\)\(x\) + \(rac{5}{2}\)On comparing with y = m\(x\) + c, we see that slope of given line = \(rac{3}{2}\)As the required line is perpendicular to the given line, ... - 4)⇒ 3(y - 5) = - 2\(x\) + 8 ⇒ 3y - 15 = -2\(x\) + 8 ⇒ 3y + 2\(x\) - 23 = 0

Description : The line x – 4y = 6 is the perpendicular bisector of the segment AB and the co-ordinates of B are (1, 3). Find the co-ordinates of A. -Maths 9th

Last Answer : Co-ordinates of A are \(\bigg(rac{3 imes9+1 imes5}{3+1},rac{3 imes6+1 imes-2}{3+1}\bigg)\) = \(\bigg(rac{32}{4},rac{16}{4}\bigg)\), i.e. (8, 4)Now, \(x\) - 3y + 4 = 0 ⇒ -3y = -\(x\) - 4 ⇒ y = \(rac{x}{3}+rac{4} ... 8) [Using, y - y1 = m (x - x1)]⇒ 3y - 12 = \(x\) - 8 ⇒ 3y - \(x\) = 4.

Description : What is the equation of the straight line passing through the point (4, 3) and making intercepts on the co-ordinates axes whose sum is –1 ? -Maths 9th

Last Answer : Diagonals of a rhombus bisect each other at right angles ⇒ Co-ordinates of mid-points of AC and BD are equal∴ 0 = \(\bigg(rac{4+(-2)}{2},rac{-5+(-1)}{2}\bigg)\) = (1, -3)Slope of BD = \(rac{-5+1}{4+2}\) = \(rac{-4}{6}\) ... (rac{3}{2}\) isy + 3 = \(rac{3}{2}\) (x - 1)⇒ 2y + 6 = 3x - 3 ⇒ 2y = 3x - 9.

Description : If A(3, 5), B(– 5, – 4), C(7, 10) are the vertices of a parallelogram taken in order, then the co-ordinates of the fourth vertex are: -Maths 9th

Last Answer : (c) RhombusCo-ordinates of P are \(\bigg(rac{-1-1}{2},rac{-1+4}{2}\bigg)\)i.e, \(\big(-1,rac{3}{2}\big)\)Co-ordinates of Q are \(\bigg(rac{-1+5}{2},rac{4+4}{2}\bigg)\)i.e, (2, 4)Co-ordinates of R ... \sqrt{(2-2)^2+(4+1)^2}\) = \(\sqrt{25}\) = 5⇒ PR ≠ SQ ⇒ Diagonals are not equal ⇒ PQRS is a rhombus.

Description : If the co-ordinates of the mid-points of the sides of a triangle are (1, 1), (2, –3), (3, 4), find its incentre. -Maths 9th

Last Answer : (b) 3 : 2 ; m = \(-rac{2}{5}\)Let P(m, 6) divides AB in the ratio k : 1. Then co-ordinates of P are \(\bigg(\)\(rac{2k-4}{k+1}\), \(rac{8k+3}{k+1}\)\(\bigg)\)Given, co-ordinates of P are (m, 6) ⇒\(rac{2k-4}{k+1} ... 2}-4}{rac{3}{2}+1}\) = \(rac{3-4}{rac{5}{2}}\) = \(rac{-2}{5}\)∴ m = \(rac{-2}{5}\).

Description : If the points with the co-ordinates {a, ma}, {b, (m + 1)b}, {c, (m + 2)c} are collinear, then which of the following is correct ? -Maths 9th

Last Answer : (d) (7, -2)Let the co-ordinates of R be (x, y). As can be easily seen, it is a point of external division Also, PR = 2QR⇒ R divides the join of P and Q externally in the ratio 2:1. ∴ x = \(rac{2 imes2-1 imes-3}{2-1}\), ... }{2-1}\)⇒ x = 4 + 3 = 7 and y = 2 - 4 = -2. ∴ Co-ordinates of R are (7, -2).

Description : What are the co-ordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 ? -Maths 9th

Last Answer : (d) 2x + 9y + 7 = 0PS being the median of ΔPQR, S is the mid-point of QR, i.e., Coordinates of S ≡ \(\bigg(rac{6+7}{2},rac{-1+3}{2}\bigg)\) = \(\bigg(rac{13}{2},1\bigg)\)Slope of line parallel to PS = Slope of PS= \(rac{1 ... y + 1) = \(rac{-2}{9}\)(x - 1), i.e., 9y + 9 = - 2x + 2 ⇒ 2x + 9y + 7 = 0.

Description : The co-ordinates of P and Q are (–3, 4) and (2, 1) respectively. -Maths 9th

Last Answer : (b) \(rac{\pi}{4}\)\(x\) cos θ + y sin θ = 2 ⇒ y sin θ = 2 - \(x\) cos θ ⇒ y = - \(x\) cot θ + 2 ⇒ Slope of this line = - cot θ Also, given \(x\) - y = 3 ⇒ y = \(x\) + 3 ⇒ Slope of this ... lines are perpendicular, - cot θ x 1 = -1⇒ cot θ = 1 ⇒ cot θ = cot \(rac{\pi}{4}\) ⇒ θ = \(rac{\pi}{4}\)

Description : Find the co-ordinate where the equation 2x + 3y = 6 intersects x-axis. -Maths 9th

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Description : Write the linear equation represented by line AB and PQ. Also find the co-ordinate of intersection of line AB and PQ. -Maths 9th

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Description : Draw the bar graph of linear equation whose solution are represented by the points having difference the co-ordinate as 25 units -Maths 9th

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Description : If (–5, 4) divides the line segment between the co-ordinate axes in the ratio 1 : 2, then what is its equation ? -Maths 9th

Last Answer : (d) x = yThe equations of the given lines are: 4x + 3y = 12 ...(i) 3x + 4y = 12 ...(ii) Solving the simultaneous equations (i) and (ii), we get\(x\) = \(rac{12}{7}\), y = \(rac{12}{7}\)∴ Point of the ... )isy - 0 = \(\bigg(rac{rac{12}{7}-0}{rac{12}{7}-0}\bigg)\) (x - 0), i.e., y = x.

Description : The straight line ax + by + c = 0 and the co-ordinate axes form an isosceles triangle under which of the following conditions ? -Maths 9th

Last Answer : (a) | a | = | b | The equation of line AB, i.e., ax + by + c = 0 in intercept form is ax + by = - c⇒ \(rac{x}{\big(-rac{c}{a}\big)}\) + \(rac{x}{\big(-rac{c}{b}\big)}\) = 1Δ AOB is isosceles Δ if OA = OB, i.e., ... \(rac{-c}{a}\) = \(rac{-c}{a}\) ⇒ \(rac{1}{a}\) = \(rac{1}{a}\) ⇒ | a | = | b |.

Description : Find the point on the curve `y^2dot` `8xdot` for which the abscissa and ordinate change at the same rate.

Last Answer : Find the point on the curve `y^2dot` `8xdot` for which the abscissa and ordinate change at the same rate.

Description : Pick up the correct statement from the following: (A) If the slope of the curve of a mass diagram in the direction of increasing abscissa is downward, it indicates an embankment (B) The ... and the next forward maximum ordinate represents the whole volume of a cutting (D) All the above

Last Answer : (D) All the above

Description : Abscissa of all the points on the X-axis is -Maths 9th

Last Answer : (d) Abscissa of all the points on the X-axis is any number because X-axis is a number line which contains many real numbers on it.

Description : If the coordinates of the two points are P(-2, 3) and Q(-3, 5), then (Abscissa of P) – (Abscissa of Q) is -Maths 9th

Last Answer : (b) We have, points P(- 2, 3) and Q(- 3, 5) Here, abscissa of Pi.e., x-coordinate of Pis -2 and abscissa of Q i.e., x-coordinate of Q is -3. So, (Abscissa of P) – (Abscissa of Q) = - 2 - (-3) = -2 + 3 =1.

Description : Abscissa of a point is positive in -Maths 9th

Last Answer : (b) Abscissa of a point is positive in I and IV quadrants.

Description : Abscissa of all the points on the X-axis is -Maths 9th

Last Answer : (d) Abscissa of all the points on the X-axis is any number because X-axis is a number line which contains many real numbers on it.

Description : If the coordinates of the two points are P(-2, 3) and Q(-3, 5), then (Abscissa of P) – (Abscissa of Q) is -Maths 9th

Last Answer : (b) We have, points P(- 2, 3) and Q(- 3, 5) Here, abscissa of Pi.e., x-coordinate of Pis -2 and abscissa of Q i.e., x-coordinate of Q is -3. So, (Abscissa of P) – (Abscissa of Q) = - 2 - (-3) = -2 + 3 =1.

Description : Abscissa of a point is positive in -Maths 9th

Last Answer : (b) Abscissa of a point is positive in I and IV quadrants.

Description : In which quadrant(s), the abscissa of a point is negative? -Maths 9th

Last Answer : Solution:- II and III quadrants