Description : Find the point of trisection of the line segment joining the points (1, 2) and (11, 9) ? -Maths 9th
Last Answer : Let P divide AB in the ratio k : 1. Then, co-ordinates of P are \(\bigg(rac{7k+4}{k+1},rac{7k+4}{k+1}\bigg)\)But P ≡ (-1, -1)∴ \(rac{7k+4}{k+1}\) = -1 ⇒ 7k + 4 = - k - 1 ⇒ 8k = - ... , it means that the division is external. ∴ AB is divided by P externally in the ratio \(rac{5}{8}\) : 1, i.e. 5 : 8.
Description : Points P, Q, R and S divide a line segment joining A (2, 6) and B (7, -4) in five equal parts. Find the coordinates of P and R. -Maths 9th
Last Answer : this is the ans hope its clear
Description : The line segment joining P(5, –2) and Q(9, 6) is divided in the ratio 3 : 1 by a point A -Maths 9th
Last Answer : Comparing y = 5\(x\) –7 with y = m\(x\) + c, the slope of given line = m = 5 ∴ Equation of a line parallel to y = 5\(x\) – 7 having y-intercept = –1 is y = 5\(x\) – 1.
Description : Points P,Q,R(in this order) divide the line joining the points A(-2,2) and B(2,8) into four equal parts. The coordinates of the point Q are: (a) (-1,7/2) (b) (1,13/2) (c) (0,5) (d) (5,1/2)
Last Answer : (c) (0,5)
Description : The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it. -Maths 9th
Last Answer : Given = A △ABC in which D and E are the mid-points of side AB and AC respectively. DE is joined . To Prove : DE || BC and DE = 1 / 2 BC. Const. : Produce the line segment DE to F , such that DE = ... of ||gm are equal and parallel] Also, DE = EF [by construction] Hence, DE || BC and DE = 1 / 2 BC
Description : If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel. -Maths 9th
Last Answer : According to question prove that the two chords are parallel.
Last Answer : Given : E and F are mid points of 2 chords AB and CD respectively. Line EF passes through centre. To prove : AB||CD ∠ OFC = ∠ OEA = 90° as line drawn through the centre to bisect the ... EF as traversal for lines AB and CD as alternate interior angles on same side are equal. Therefore, AB || CD
Description : Prove that the line segment joining the mid-points of the diagonals of a trapezium is parallel to the parallel sides and equal to half of their difference. -Maths 9th
Last Answer : In a parallelogram ABCD, the bisector of ∠ A also bisects BC at X.Prove that AD = 2AB.
Description : In what ratio is the line joining the points A(4, 4) and B(7, 7) divided by P(–1, –1)? -Maths 9th
Last Answer : Let ABCD be the given square and let A ≡ (3, 4) and C ≡ (1, -1). Also let B ≡ (x, y). ABCD being a square,AB = BC ⇒ AB2 = BC2, ∠ABC = 90º⇒ \(\big(\sqrt{(x-3)^2+(y-4)^2}\big)^2\) = \(\big(\sqrt{(x-1)^2+(y+1 ... \(rac{9}{2}\),\(rac{1}{2}\)\(\bigg)\)and \(\bigg(\)\(-rac{1}{2}\), \(rac{5}{2}\)\(\bigg)\)
Description : Plot the points P(1, 0), Q(4, 0) and 5(1, 3). Find the coordinates of the point R such that PQRS is a square. -Maths 9th
Last Answer : see the below answer
Description : The point which divides the line segment joining the points (7, –6) and (3, 4) in the ratio 1 : 2 lies in the: (a) I quadrant (b) II quadrant (c) III quadrant (d) IV quadrant
Last Answer : (d) IV quadrant
Description : The ratio in which the line 3x + 4y = 7 divides the line joining the points (–2, 1) and (1, 2) is -Maths 9th
Last Answer : (a) (–24, –2)Co-ordinates of the point of external division are\(\bigg(rac{m_1\,x_2-m_2\,x_1}{m_1-m_2},rac{m_1y_2-m_2y_1}{m_1-m_2}\bigg)\), i.e.,∴ Required point = \(\bigg(rac{3 imes-6-2 imes4}{3-2},rac{3 imes2-2 imes4}{3-2}\bigg)\)= \(\big(rac{-24}{1},rac{-2}{1}\big)\), i.e., (–24, –2).
Description : Find the coordinates of the point which divides the join of the points (8, 9) and (–7, 4) internally in the ratio 2 : 3. -Maths 9th
Last Answer : The circumcentre of a triangle is equidistant from the vertices of a triangle. Let A(3, 0), B(-1, -6), and C(4, -1) be the vertices of ΔABC and P(x, y) be the circumcentre of this triangle. Then, PA = PB = PC ⇒ PA2 = PB2 = ... PC = \(\sqrt{(1-3)^2+(-3-0)^2}\) = \(\sqrt{4+9}\) = \(\sqrt{13}\) units.
Description : The mid-point of the line joining the points (–10, 8) and (–6, 12) divides the line joining the points (4, –2) and (– 2, 4) in the ratio -Maths 9th
Last Answer : (d) 2 : 1 externallyThe mid-point of the line joining the points (-10, 8) and (- 6, 12) is\(\bigg(rac{-10+(-6)}{2},rac{8+12}{2}\bigg)\), i.e., (-8, 10).Let (-8, 10) divide the join of (4 ... 6k = 12 ⇒ k = -2 Since the value of k is negative, it is a case of external division and the ratio is 2 : 1.
Description : The ratio in which P ( , B(2,-5) is : (a) 1:5 (b) 5:1 ) divides the line segment joining the points A ( , (c) 1:4 ) and (d) 4:1
Last Answer : (a) 1:5
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 : If the coordinates of two points are P( -2,3) and Q ( -3, 5) then find (abscissa of P)–(abscissa of Q) -Maths 9th
Last Answer : Abscissa of P – Abscissa of Q = (–2) – (–3) = –2 + 3 = 1.
Description : Write the coordinates of each of the points P, Q, R, S, T and 0 from the figure . -Maths 9th
Last Answer : Here, points P and S lie in I quadrant so their both coordinates will be positive. Now, perpendicular distance of P from both axes is 1, so coordinates of P are (1, 1). Also, perpendicular distance of S ... 0 is the intersection of both axes, so it is the origin and its coordinates are O (0,0).
Description : Two congruent circles intersect each other at point A and B.Through A any line segment PAQ is drawn so that P,Q lie on the two circles.Prove that BP = BQ. -Maths 9th
Last Answer : Solution :- Let, O and O' be the centres of two congruent circles. As, AB is the common chord of these circles. ∴ ACB = ADB As congruent arcs subtent equal angles at the centre. ∠AOB = ∠AO'B ⇒ 1/2∠AOB = 1/2∠AO'B ⇒ ∠BPA = ∠BQA ⇒ BP = BQ (Sides opposite to equal angles)
Description : ABCD is a square. P, Q, R, S are the mid-points of AB, BC, CD and DA respectively. By joining AR, BS, CP, DQ, we get a quadrilateral which is a -Maths 9th
Last Answer : According to the given statement, the figure will be a shown alongside; using mid-point theorem: In △ABC,PQ∥AC and PQ=21 AC .......(1) In △ADC,SR∥AC and SR=21 AC .... ... are perpendicular to each other) ∴PQ⊥QR(angle between two lines = angle between their parallels) Hence PQRS is a rectangle.
Description : 6. Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other. -Maths 9th
Last Answer : Solution: Let ABCD be a quadrilateral and P, Q, R and S are the mid points of AB, BC, CD and DA respectively. Now, In ΔACD, R and S are the mid points of CD and DA respectively. , ... , PQRS is parallelogram. PR and QS are the diagonals of the parallelogram PQRS. So, they will bisect each other.
Description : Two points with coordinates (3, 4) and (–5, 4) lie on a line parallel to which axis? Justify your answer. -Maths 9th
Last Answer : Solution :- y-coordinate of both the points is 4. So, both points lie on the line y = 4 which is parallel to x-axis.
Description : The midpoint of the line segment joining the points B and D is: (a) (10,11) (b) (11,5) (c) (7/2,11/2) (d) (5,11/2)
Last Answer : (c) (7/2,11/2)
Description : The point which lies on the perpendicular bisector of the line segment joining the points B(3,5) is: (a) (-3,0) (b) (5,0) (c) (5,-5) (d) (0,0)
Last Answer : (d) (0,0)
Description : The point (-1,2) divides the line segment joining the points A(2,5) and B(x,y) in the ratio 3:4, then the value of x2 + y2 is : (a) 27 (b) 28 (c) 29 (d) 30
Last Answer : (c) 29
Description : Find the ratio in which the x-axes divides the line joining the points (–2, 5) and (1, –9) ? -Maths 9th
Last Answer : Let the co-ordinates of the point of internal division A be (x, y). Then,\(x\) = \(rac{2 imes(-7)+3 imes8}{2+3}\) = \(rac{-14+24}{5}\) = \(rac{10}{5}\) = 2y = \(rac{2 imes4+3 imes9}{2+3}\) = \(rac{8+27}{5}\) = \(rac{35}{5}\) = 7∴ Co-ordinates of the point for internal division are (2, 7).
Description : In what ratio is the line joining the points (2, –3) and (5, 6) divided by the x-axis. -Maths 9th
Last Answer : (b) (2, 1) (- 2, 1)Let PQRS be the required square and P(0, -1) and R(0, 3) be its two opposite vertices. Length of diagonal PR = \(\sqrt{(0-0)^2+(3+1)^2}\) = \(\sqrt{16}\) = 4∴ Length of each side = \( ... + 4 = 8 ⇒ a2 = 4 ⇒ a = 2. ∴ The other two vertices of the square are (+2, 1) and (-2, 1).
Description : Which axis is parallel to the line on which the two points with coordinates (4, 3) and (4,–2) lie? -Maths 9th
Last Answer : Solution :- As x-coordinate of both points is 4. So, both points lie on the line x = 4 which is parallel to y-axis.
Description : Prove that the line joining the mid-points of two parallel chords of a circle passes through the centre. -Maths 9th
Last Answer : Let AB and CD be two parallel chords having P and Q as their mid-points, respectively. Let O be the centre of the circle. Join OP and OQ and draw OX | | AB | | CD. Since, Pis the mid-point of AB. ⇒ OP ... 90° Now, ∠POX + ∠XOQ = 90° + 90° = 180° so, POQ is a straight line . Hence proved
Description : Prove that the line joining the mid-points of the diagonals of a trapezium is parallel to the parallel sides of the trapezium. -Maths 9th
Last Answer : Given Let ABCD be a trapezium in which AB|| DC and let M and N be the mid-points of the diagonals AC and BD, respectively.
Description : Find the coordinates of the point which divides externally the join of the points (3, 4) and (– 6, 2) in the ratio 3 : 2. -Maths 9th
Last Answer : (d) D lies on the boundary of ΔABC∵ Mid-point of BC = \(\bigg(rac{7+3}{2},rac{7+5}{2}\bigg)\), i.e, (5, 6). we can easily show that D lies on the boundary of ΔABC.
Description : In Fig. 10.20, two circles intersects at two points A and B.AD and AC are diameters to the circles. Prove that B lies on the line A segment DC. -Maths 9th
Last Answer : Solution :- Jion AB ∠ABD = 90° (Angle in a semicircle) Similarly, ∠ABC = 90° So, ∠ABD + ∠ABC = 90° + 90° = 180° Therefore,DBC is a line i.e.,B lies on the segment DC.
Description : A straight line passes through the points (a, 0) and (0, b). The length of the line segment contained between the axes is 13 and the product of -Maths 9th
Last Answer : (d) \(rac{23}{\sqrt{17}}\)The given lines are:L : \(rac{x}{5}+rac{y}{b}=1\) ....(i)K : \(rac{x}{c}+rac{y}{3}=1.\) ...(ii)Since line L passes through (13, 32),\(rac{13}{ ... between parallel lines ax + by + c1 = 0 and ax + by c2 = 0 is d = \(rac{|c_2-c_1|}{\sqrt{a^2+b^2}}\bigg)\)
Description : The endpoint A of a line segment AB is (3 , -1). If midpoint of AB is (5,7) then the coordinates of the point B are: (a) (7,13) (b) (7,15) (c) (4,3) (d) (4,4)
Last Answer : (b) (7,15)
Description : A(5,0) and B(0,8) are two vertices of triangle OAB. a). What is the equation of the bisector of angle OAB. b). If E is the point of intersection of this bisector and the line through A and B,find the coordinates of E. Hence show that OA:OB = AE:EB -Maths 9th
Last Answer : NEED ANSWER
Last Answer : This answer was deleted by our moderators...
Description : Consider a window bounded by the lines : x = 0; y= 0; x = 5 and y = 3. The line segment joining (–1, 0) and (4, 5), if clipped against this window will connect the points (A) (0, 1) and (2, 3) (B) (0, 1) and (3, 3) (C) (0, 1) and (4, 3) (D) (0, 1) and (3, 2)
Last Answer : (A) (0, 1) and (2, 3)
Description : How do I find the midpoint of the line segment joining the points (-1,3) and (-9,8)?
Last Answer : 85
Description : On plotting the points 0(0, 0), A(3, 0), 5(3, 4), C(0, 4) and joining OA, AB, BC and CO. -Maths 9th
Last Answer : (b) Here, point 0 (0, 0) is the origin. A(3, 0) lies on positive direction of X-axis, B (3, 4) lies in 1st quadrant and C (0, 4) lines on positive direction of Y-axis. On joining OA AB, BC and CO the figure obtained is a rectangle.
Description : Write the coordinates of two points on X-axis and two points on Y-axis which are at equal distances from the origin. Connect all these points and make them as vertices of quadrilateral. Name the quadrilateral thus formed. -Maths 9th
Last Answer : Let a be the equal distance from origin on both axes. Now, the coordinates of two points on equal distance 'a'on x-axis are Pla, 0) and R(-a, 0). Also, the coordinates of two points on equal distance 'a' on Y-axis are Q(0, a) and S(0, -a). Join all the four points on the graph.
Description : Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units. -Maths 9th
Last Answer : As per question, the sum of the coordinates is 10 units. Let x and y be two coordinates, then we get x + y = 10. For x = 5, y = 5, therefore, (5, 5) lies on the graph of x + y = 10. For x = ... and (3, 7) on the graph paper and joining them by a line, we get graph of the linear equation x + y = 10.