1.
The distance of the point P(2, 3) from the x-axis is
(a) 2
(b) 3
(c) 1
(d) 5
2. The distance between the point P(1, 4) and Q(4, 0) is
(a) 4
(b) 5
(c) 6
(d) 3√3
3. The points (-5, 1), (1, p) and (4, -2) are collinear if
the value of p is
(a) 3
(b) 2
(c) 1
(d) -1
4. The area of the triangle ABC with the vertices A(-5, 7), B(-4, -5) and C(4, 5) is
(a) 63
(b) 35
(c) 53
(d) 36
5. The distance of the point (α, β) from the origin is
(a) α + β
(b) α² + β²
(c) |α| + |β|
(d) α2+β2−−−−−−√
6. The area of the triangle whose vertices are A(1, 2), B(-2, 3) and C(-3, -4) is
(a) 11
(b) 22
(c) 33
(d) 21
7. The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates
of point of trisection are
(a) (3, 3)
(b) (- 3, 3)
(c) (3, – 3)
(d) (-3,-3)
8. The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally
in the ratio
(a) 3 : 4
(b) 3 : 2
(c) 2 : 3
(d) 4 : 3
9. The distance between A (a + b, a – b) and B(a – b, -a – b) is
10. If (a/3, 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3),
then the value of ‘a’ is
(a) 12
(b) -6
(c) -12
(d) -4
11. If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is
(a) -7 or -1
(b) -7 or 1
(c) 7 or 1
(d) 7 or -1
12. The points (1,1), (-2, 7) and (3, -3) are
(a) vertices of an equilateral triangle
(b) collinear
(c) vertices of an isosceles triangle
(d) none of these
13. The coordinates of the centroid of a triangle whose vertices are (0, 6), (8,12) and
(8, 0) is
(a) (4, 6)
(b) (16, 6)
(c) (8, 6)
(d) (16/3, 6)
14. Two vertices of a triangle are (3, – 5) and (- 7,4). If its centroid is (2, -1), then the
third vertex is
(a) (10, 2)
(b) (-10,2)
(c) (10,-2)
(d) (-10,-2)
15. The area of the triangle formed by the points A(-1.5, 3), B(6, -2) and C(-3, 4) is
(a) 0
(b) 1
(c) 2
(d) 3/2
16. If the points P(1, 2), B(0, 0) and C(a, b) are collinear, then
(a) 2a = b
(b) a = -b
(c) a = 2b
(d) a = b
17. A triangle with vertices (4, 0), (- 1, – 1) and (3, 5) is a/an
(a) equilateral triangle
(b) right-angled triangle
(c) isosceles right-angled triangle
(d) none of these
18. The points (- 4, 0), (4, 0) and (0, 3) are the vertices of a/an [NCERT Exemplar
Problems]
(a) right triangle
(b) isosceles triangle
(c) equilateral triangle
(d) scalene triangle
19. A circle drawn with origin as the centre passes through , (132,0). The point which
does not lie in the interior of the circle is [NCERT Exemplar Problems]
20. If the distance between the points(4, p) and (1, 0) is 5 units, then the value of p is
[NCERT Exemplar Problems]
(a) 4 only
(b) ± 4
(c) -4 only
(d) 0
21. The points (2, 5), (4, – 1) and (6, – 7) are vertices of an/a
(a) isosceles triangle
(b) equilateral triangle
(c) right-angled triangle
(d) none of these
22. If the segment joining the points (a, b) and (c, d) subtends a right angle at the
origin, then
(a) ac – bd = 0
(b) ac + bd = 0
(c) ab + cd = 0
(d) ab – cd= 0
23. AOBC is a rectangle whose three vertices are A(0, 3), 0(0, 0) and B(5, 0). The
length of its diagonal is [NCERT Exemplar Problems]
(a) 5
(b) 3
(c) √34
(d) 4
24. The perimeter of a triangle with vertices (0,4), (0, 0) and (3, 0) is [NCERT Exemplar
Problems]
(a) 5
(b) 12
(c) 11
(d) 7 + √5
25. If the distance between the points (4, p) and (1, 0) is 5 units, then the value of p is
[NCERT Exemplar Problems]
(a) 4 only
(b) ±4
(c) -4 only
(d) 0
26. If p(a3,4) is the mid-point of the line segment joining the points Q (-6, 5) and R (-
2, 3), then the value of a is [NCERT Exemplar Problems]
(a) -4
(b) -12
(c) 12
(d) -6
27. If P(l, 2), Q(4, 6), R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS, then
(a) a = 2,b = A
(b) a = 3,b = 4
(c) a = 2, b = 3
(d) a = 3, b = 5
28. The point P which divides the line segment joining the points A(2, -5) and B(5, 2)
in the ratio 2 : 3 lies in the quadrant
(a) I
(b) II
(c) III
(d) IV
29. The points (k + 1, 1), (2k + 1, 3) and (2k + 2, 2k) are collinear if
(a) k = -1, 2
(b) k=12,2
(c) k = 2, 1
(d) k = –12,2
30. The area of the triangle with vertices at the points (a, b + c), (b, c + a) and (c, a +
b) is
(a) (a + b + c) sq. units
(b) (a + b – c) sq. units
(c) (a – b + cj sq. units
(d) 0
