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Mathematics : Coordinate Geometry

Short Answer Type

301. Find the co-ordinates of the points which divide the line segment joining the points (-2, 0) and (0, 8) in four equal parts.

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302. Equilateral triangles are drawn on the sides of a right-angle triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

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303. Find the co-ordinates of the points equidistant from the points A(-2, -3), B(-1, 0) and C(7, -6)

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304. Two vertices of a ∆ABC are given by A(2, 3) and B(-2, 1) and its centroid is a

open parentheses 1 comma space 2 over 3 close parentheses

Find the co-ordinates of the third vertex C of the ∆ABC.

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305. Two vertices of a ∆ABC are given by A(6, 4) and B(-2, 2) and its centroid is C(3, 4). Find the coordinates of the third vertex C of the ∆ABC.

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306. Find the co-ordinates of the point equidistant from three given points A(5, 1), B(-3, -7) and C(7, -1).

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307. Find the value of p for which the points (-1, 3) (2, p) and (5, -1) are collinear.

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308. Find the co-ordinates of the point equidistant from three given points A(5, 3), B(5, -5) and C(1, -5).

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309. Find the value of p for which points (-5, 1), (1, p) and (4, -2) are collinear.

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310. In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by the y-axis? Also find the co-ordinates of the point of division.

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