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Coordinate Geometry

Short Answer Type

221. In what ratio does the like x - y - 2 = 0 divides the line segment joining (3, -1) and (8, 9) ?

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222. Find the ratio in which the point (x, -1) divides the line segment joining the points (-3, 5) and (2, -5). Also find the value of x

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223. Find the ratio in which the point (2, y) divides the line segment joining the points A(-2, 2) and B (3, 7). Also find the value of y.

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224. In what ratio does the point P(2, -5) divide the line segment joining A(-3, 5) and B (4, -9)?

Let the point P divide AB in the ratio K : 1. Then the co-ordinate of C are

equals space straight C space open square brackets fraction numerator straight K left parenthesis 4 right parenthesis plus 1 left parenthesis negative 3 right parenthesis over denominator straight K plus 1 end fraction comma space fraction numerator straight K left parenthesis negative 9 right parenthesis plus 1 left parenthesis 5 right parenthesis over denominator straight K plus 1 end fraction close square brackets equals space straight C space open square brackets fraction numerator 4 straight K minus 3 over denominator straight K plus 1 end fraction comma space fraction numerator negative 9 straight K plus 5 over denominator straight K plus 1 end fraction close square brackets

But, the co-ordinates of C are given as (2, -5)

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Hence, the point P divides AB in the ratio 5 : 2.

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225. The mid-points of the sides of a triangle are (3, 4), (4, 6) and (5, 7). Find the coordinates of the vertices of the triangle.

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226. Determine the ratio in which the line 3x + 4y - 9 = 0 divides the line segment joining the points (1, 3) and (2, 7)

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227. A line segment joining the points P(3, 3) and Q(6, - 6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

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228. Find the area of the quadrilateral w hose vertices are A(0, 0), B(6, 0), C(4, 3) and D(0, 3).

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229. Find the area of the quadrilateral whose vertices, taken in order are (-4, -2), (-3, -5), (3, -2) and (2, 3).

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230. Find the value of ‘K’ if the points (K, 3), (6, -2) and (-3, 4) are collinear.

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