Maths Book back answers and solution for Exercise questions - Mathematics : Coordinate Geometry : Problem Questions with Answer

**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 3*x* + *y*
− 2 = 0 , 5*x* + 2*y* − 3 = 0 and 2*x* − *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*
+ 3*y* = 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 4*x* + 7*y* − 3 = 0 and 2*x* − 3*y*
+ 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 2*x* − 3*y* + 4 = 0 and 3*x*
+ 4*y* − 5 = 0 seek to reach the path whose equation is 6*x* − 7*y*
+ 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

Tags : Problem Questions with Answer, Solution | Mathematics , 10th Mathematics : Coordinate Geometry

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10th Mathematics : Coordinate Geometry : Exercise: Coordinate Geometry | Problem Questions with Answer, Solution | Mathematics

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