# Class 10 – Coordinate Geometry – Important Questions

Important Questions Previous Years Questions**Coordinate Geometry – Important Questions**

**Find a relation between x and y such that the point (x , y) is equidistant from the points (7, 1) and (3, 5).****Find the distance between the following pairs of points :****(2, 3), (4, 1)****(-6, 2), (-4, -3)****(7, 6), (2, 1)****(4, -3), (2, -8)****(a, b), (– a, – b)**

**Check whether (7, – 4), (7, 5) and (6, – 1) are the vertices of an isosceles triangle.****Find the ratio in which the point P (3/4, 5/12) divides the line segment joining the points A (1/2, 3/2) and B (2, -5).****Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:****(– 1, – 2), (1, 0), (– 1, 2), (– 3, 0)****(–3, 5), (3, 1), (0, 3), (–1, – 4)**

**If the points (x,y) is equidistant from the points (a+b, b-a) and (a-b, a+b), prove that bx = ay.****Find the relation between x and y if points (2, 1), (x, y) and (7, 5) are collinear**.**Find the value of x for which the distance between the points P (4, -5) and Is 10 units.****Find the ratio in which point (x, 2) divides the line segment joining points (-3, -4) and (3, 5). Also find the value of x.****Find the value of k if the points A(2, 3), B(4, k) and C(6, –3) are collinear.****Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.****If the points A (1, –2), B (2, 3) C (a, 2) and D (– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as the base.****Find the point of y-axis which is equidistant from the points (-5, -2) and (3, 2).****Find the coordinates of the points which divides the line segment joining the points (-2,0) and (0,8) in four equal parts.****Point P (5, -3) is one of the two points of trisection of the line segment joining the points A (7, -2) and B (1, -5) near to A. Find the coordinates of the other point of trisection.****Show that the point P (-4, 2) lies on the line segment joining the points A (-4 , 6) and B (-4, -6).****If A (-2, 4) ,B (0, 0) , C (4, 2) are the vertices of a ∆ABC, then find the length of median through the vertex A.****Find the coordinates of a point A, where AB is diameter of a circle whose centre is (2, -3) and B is (1, 4).****If the point A(1,2), B(0,0) and C(a,b)are collinear, then find the relation between a and b.****Find k so that the point P(-4,6) lies on the line segment joining A (k,0) and B (3, -8). Also find the ratio in which P divides AB.****Two opposite vertices of a square are (-1,2) and (3, 2). Find the coordinates of the other two vertices.****If the points (x,y) ,(-5,-2) and (3,-5) are collinear, then prove that 3x+8y+31 = 0.****Find the ratio in which the Y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also find the coordinates of the point of division.****Find the centre of a circle passing through the points (6,-6), (3, 7) and (3, 3).****Points P, Q , R, and S in that order are dividing a line segment joining A (2, 6) and B (7, -4) in five equal parts. Find the coordinates of point P and R ?**

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