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Coordinate Geometry

Short Answer Type

271. Determine the ratio in which the line 2x + 3y - 30 = 0 divides the join of A(3, 4) and B(7, 8). Also find the co-ordinates of the point of division.

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272. The mid-points of the sides of a triangle have co-ordinates

open parentheses fraction numerator 1 over denominator 2 comma space end fraction comma 11 over 2 close parentheses open parentheses 5 comma 3 over 2 close parentheses space and space open parentheses fraction numerator negative 5 over denominator 2 end fraction comma 2 close parentheses

Find the co-ordinates of the vertices of the triangle.

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273. If ‘a’ is the length of one of the sides of an equilateral ∆ABC, base BC lies on x-axis and vertex B is at origin. Find the co-ordinates of the vertices of ∆ABC.

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274. Find the value of ‘m’ for which the points with co-ordinates (3, 5), (m, 6) and

open parentheses 1 half comma space 15 over 2 close parentheses space space

are collinear.

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275. (-2, 2), (x. 8) and (6, y) are three concyclic points, whose centre is (2. 5), find the possible values of x and y.

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276. Find the lengths of the medians of the triangle whose vertices are (1, 1), (0, 4) and (-5. 3).

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277. Find the vertices of the triangle, the mid-points of whose sides are (3, 1), (5, 6) and (-3, 2).

Solution not provided.

Ans. (-1, 7), (-5, -3), (11, 5)

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278. The given fig. (7. 41) shows points A and B on x-axis and y-axis respectively.

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279.

The co-ordinates of points A and B are (1, 2) and (2, 3) respectively.
Find the co-ordinates of point P. in AB. so that AP : PB 4 : 3.

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280. Find the co-ordinates of the centre of the circle passing through the points (0, 0), (-2, 1) and (-3, 2). Also, find its radius.

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