Exercise: Coordinate Geometry

Unit Exercise

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.

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

4. If vertices of a 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.

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

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

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?

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.

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.

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.

Answers:

1. Rhombus

2. (7/2, 13/2)

3. 0 sq.units

4. -5

6. 2x − 3y − 6 = 0, 3x − 2y + 6 = 0

7. 1340 litres

8. (- 1, -4)

9. 13x + 13y − 6 = 0

10. 119x + 102y −125 = 0