If the three points (k, 2k), (2k, 3k) and (3, 1) are collinear then k is equal to -Maths 9th

If the three points (k, 2k), (2k, 3k) and (3, 1) are collinear then k is equal to -Maths 9th
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1 Answer

Answer :

(d) 3Let (x, y) be the co-ordinates of the third vertex of the triangle. Then\(rac{0+2+x}{3}\) = 1 and \(rac{0+0+y}{3}\) = 1⇒ 2 + \(x\) = 3 and y = 3 ⇒ \(x\) = 1, y = 3. ∴ Co-ordinates of vertices of the triangle are (0, 0), (2, 0) and (1, 3). ∴ Area of triangle = \(rac{1}{2}\) [0(0 – 3) + 2(3 – 0) + 1(0 – 0)][∵Area of Δ = \(rac{1}{2}\) (x1(y2 – y3) + x2 (y2 – y3) + x3(y1 – y2)]= \(rac{1}{2}\) [0+6+0] = \(rac{6}{2}\) = 3.
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Related questions

For a given material, if E, C, K and m are Young's modulus, shearing modulus, bulk modulus and Poisson ratio, the following relation does not hold good (A) E = 9KC/3K + C (B) E = 2K (1 + 2/m) (C) E = 2C (1 + 1/m) (D) E = 3C (1 - 1/m)

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Description : If the points A(1, 2), B(0, 0) and C(a, b) are collinear, then -Maths 9th

Last Answer : (a) - 2For three points to be collinear, area of the triangle formed by the three points should be equal to zero, i.e.\(rac{1}{2}\) [k(3k - 1) + 2k(1 - 2k) + 3(2k - 3k)] = 0⇒ \(rac{1}{2}\) [3k2 - k + ... = 0 or -2 Neglecting k = 0, as then (k, 2k) and (2k, 3k) will be the same point, we take k = -2.

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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).

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An animal drawn seed drill has k number of furrow openers 180mm apart. If the speed of the operation is 2.0kmph then the area covered (ha), in 8 hr day is given by: a) 1.85/1000k b) 28.8 * 10-2k c) k/6.456 d) 1.762k

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Description : Let ABC be a triangle. Let D, E, F be points respectively on segments BC, CA, AB such that AD, BE and CF concur at point K. -Maths 9th

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Description : If the area of the quadrilateral whose angular points A, B, C, D taken in order are (1, 2), (–5, 6), (7, – 4) and (–2, k) be zero, -Maths 9th

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The slope of a line perpendicular to the line which passes through the points (–k, h) and (b, – f ) is -Maths 9th

Description : The slope of a line perpendicular to the line which passes through the points (–k, h) and (b, – f ) is -Maths 9th

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A semi-circle of diameter 14 cm has three chords of equal length connecting the two end points of the diameter so as -Maths 9th

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Description : if A,Band c are three points on a line and B lies between A and C then prove that AB+BC=AC -Maths 9th

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if A,Band c are three points on a line and B lies between A and C then prove that AB+BC=AC -Maths 9th

Description : if A,Band c are three points on a line and B lies between A and C then prove that AB+BC=AC -Maths 9th

Last Answer : AB=AC-BC BC =AC-AB AB+BC=AB HENCE PROVED

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Description : If P, Q and R are three points on a line and Q is between P and R,then prove that PR - QR= PQ. -Maths 9th

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What is -k + 3k?

Description : What is -k + 3k?

Last Answer : It is -57k + 324

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Description : Walls of a cubical oven are of thickness l, and they are made of material of thermal conductivity k. The temperature inside the oven is 100°C and the inside heat transfer co-efficient is 3k/l'. If the wall temperature ... wall temperature in degree centigrade? (A) 35.5 (B) 43.75 (C) 81.25 (D) 48.25

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Description : For what value of p is the coefficient of x^2 in the product (2x – 1) (x – k) (px + 1) equal to 0 and the constant term equal to 2 ? -Maths 9th

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Description : In the given figure, equal chords AB and CD of a circle with centre O cut at right angles at E. If M and N are the mid-points of AB and CD respectively, prove that OMEN is a square. -Maths 9th

Last Answer : Join OE. In ΔOME and ΔONE, OM =ON [equal chords are equidistant from the centre] ∠OME = ∠ONE = 90° OE =OE [common sides] ∠OME ≅ ∠ONE [by SAS congruency] ⇒ ME = NE [by CPCT] In quadrilateral OMEN, ... =ON , ME = NE and ∠OME = ∠ONE = ∠MEN = ∠MON = 90° Hence, OMEN is a square. Hence proved.

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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

In the given figure, equal chords AB and CD of a circle with centre O cut at right angles at E. If M and N are the mid-points of AB and CD respectively, prove that OMEN is a square. -Maths 9th

Description : In the given figure, equal chords AB and CD of a circle with centre O cut at right angles at E. If M and N are the mid-points of AB and CD respectively, prove that OMEN is a square. -Maths 9th

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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

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

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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

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.

PQ and RS are two equal and parallel line segments.Any points M not lying on PQ or RS is joined to Q and S and lines through P parallel to SM meet at N.Prove that line segments MN and PQ are equal and parallel to each other. -Maths 9th

Description : PQ and RS are two equal and parallel line segments.Any points M not lying on PQ or RS is joined to Q and S and lines through P parallel to SM meet at N.Prove that line segments MN and PQ are equal and parallel to each other. -Maths 9th

Last Answer : hope its clear

Side AC of a right triangle ABC is divided into 8 equal parts. Seven line segments parallel to BC are drawn to AB from the points of division. -Maths 9th

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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

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

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