CO.ORDINATE GEOMETRY

1. The distance of the point (α, β) from the origin is

• $\alpha\ +\ \beta$

• $\alpha^2\ +\ \beta^2$

• $\left|\alpha\right|\ \ +\left|\beta\right|$

• $\sqrt{\alpha^2+\ \beta^2}$

The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are

• (3, 3)

• (-3, 3)

• (3, -3)

• (-3, -3)

3. The distance between A (a + b, a – b) and B(a – b, -a – b) is

• $a^2\ +b^2$

• $\sqrt{a^2\ +\ b^2}$

• $2\sqrt{a^2\ +\ b^2}$

• $2\ \left(a^2\ +\ b^2\right)$

4 . If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is

• -7 or -1

• -7 or 1

• 7 or 1

• 7 or -1

5. The points (1,1), (-2, 7) and (3, -3) are

• vertices of an equilateral triangle

• collinear

• vertices of an isosceles triangle

• none of these

6. A triangle with vertices (4, 0), (- 1, – 1) and (3, 5) is a/an

• equilateral triangle

• right-angled triangle

• isosceles right-angled triangle

• none of these

7. If the distance between the points(4, p) and (1, 0) is 5 units, then the value of p is

• 4 only

• $\pm4$

• -4 only

• 0

 $8.Ifp\ \ \left(\ \frac{a}{3\ },\ 4\ \right)is\ the\ mid-point\ ofthe\ line\ segment\ joining\ the\ points\ Q(-6,5)\ and\ R(-2,3),then\ the\ value\ ofa\ \ is$  

• -4

• -12

• 12

• 6

9. If P(l, 2), Q(4, 6), R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS, then

• a = 2,b = 2

• a = 3,b = 4

• a = 2, b = 3

• a = 3, b = 5

10.Find the coordinates of a point A, where AB is diameter of a circle whose centre is (2, -3) and B is the point (1, 4).

• 3 ,-10

• -3 ,10

• 3 ,10

• -3 ,-10