**Coordinate Geometry Practice Questions for Grade 10 :**

Here we are going to see, some practice questions using different concepts of coordinate geometry.

Questions

(1) PQRS is a rectangle formed by joining the points P(-1,-1), Q(-1, 4), R(5, 4) and S(5,-1) . A, B, C and D are the mid-points of PQ, QR, RS and SP respectively. Is the quadrilateral ABCD a square, a rectangle or a rhombus? Justify your answer. Solution

(2) The area of a triangle is 5 sq.units. Two of its vertices are (2, 1) and (3, –2). The third vertex is (x, y) where y = x + 3 . Find the coordinates of the third vertex.

(3) Find the area of a triangle formed by the lines 3x + y − 2 = 0 , 5x + 2y − 3 = 0 and 2x − y − 3 = 0 Solution

(4) If vertices of quadrilateral are at A(-5, 7) , B(-4, k) , C(-1, -6) and D(4, 5) and its area is 72 sq.units. Find the value of k. Solution

(5) Without using distance formula, show that points (-2, -1) , (4, 0) , (3, 3) and (-3, 2) are the vertices of a parallelogram. Solution

(6) Find the equations of the lines, whose sum and product of intercepts are 1 and –6 respectively. Solution

(7) The owner of a milk store finds that, he can sell 980 litres of milk each week at ₹14/litre and 1220 litres of milk each week at ₹16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at ₹17/litre? Solution

(8) Find the image of the point (3,8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror Solution

(9) Find the equation of a line passing through the point of intersection of the lines 4x + 7y − 3 = 0 and 2x − 3y + 1 = 0 that has equal intercepts on the axes. Solution

(10) A person standing at a junction (crossing) of two straight paths represented by the equations 2x −3y + 4 = 0 and 3x + 4y −5 = 0 seek to reach the path whose equation is 6x −7y + 8 = 0 in the least time. Find the equation of the path that he should follow. Solution

After having gone through the stuff given above, we hope that the students would have understood, "Coordinate Geometry Practice Questions for Grade 10".

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