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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

Let the point P (x, - 1) divides the line segment joining the points A (-3, 5) and B (2, -5) in the ratio k : 1. Then

fraction numerator k m space x space left parenthesis negative 5 right parenthesis space plus space 1 space x space 5 over denominator k space plus space 1 end fraction equals space minus 1 rightwards double arrow space space fraction numerator negative 5 k space plus space 5 over denominator k space plus 1 end fraction equals negative 1 rightwards double arrow space minus 5 k space plus space 5 space equals space minus k space minus 1 rightwards double arrow space space space minus 4 k space equals space minus 6 rightwards double arrow space space space space space space k equals 6 over 4 equals 3 over 2

Hence, the required ratios is 3 : 2.

Also space space space space space space space space straight x space equals space fraction numerator 3 cross times 2 plus 2 cross times left parenthesis negative 3 right parenthesis over denominator 3 plus 2 end fraction equals fraction numerator 6 minus 6 over denominator 5 end fraction equals 0

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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)?

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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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