MULTIPLE CHOICE QUESTIONS: (MCQ’s)
1. The points (−1, –2), (1, 0), ( 1, 2), ( 3, 0) forms a quadrilateral of the type ____
(a) Square
(b) Rectangle
(c) Parallelogram
(d) Rhombus
2. If the distance between the points A(2, 2) and B(1, x) is equal to 5
then the value of x is____
(a) 2
(b) 2
(c) 1
(d) 1
3.The midpoints of a line segment joining two points A(2, 4) and B(2, 4) is____
(a) (2, 4)
(b) (2, 4)
(c) (0, 0)
(d) (2, 4)
4. The distance of point A(x, y) from the origin O (0,0) is given by OA = ___
(a) 2√x² + y²
(b) √x² + y²
(c) √x² − y²
(d) 4√x² + y²
5. The distance between the points P (0, 2) and Q (6, 0) is_____
(a) 4√10
(b) 2√10
(c) √10
(d) 20
6. If O (p/3, 4) is the midpoint of the line segment joining the
points P (6, 5) and Q (2, 3). The value of p is____
(a) 7/2
(b) 12
(c) 4
(d) 4
7. The points which divides the line segment of points P (1, 7) and
Q (4, 3) in the ratio of 2 : 3 is___
(a) (1, 3)
(b) (1, 3)
(c) (1, 3)
(d) (1, 3)
8. The ratio in which the line segment joining the points P(3, 10) and
Q(6, – 8) is divided by O(1, 6) is ____
(a) 1 : 3
(b) 3 : 4
(c) 2 : 7
(d) 2 : 5
9. The coordinates of a point P, where PQ is the diameter of circle
whose centre is O(2, – 3) and Q is (1, 4) is____
(a) (3, −10)
(b) (2, 10)
(c) (3, 10)
(d) (2, −10)
10. Find the coordinates of the point which divides the line segment joining
the points (4,−2)and (7, 4) in the ratio 3:1 internally.
(a) (15/4 , 5/2)
(b) (25/4 , 5/2)
(c) (25/4 , 7/2)
(d) (25/3 , 5/2)
11. If we prove that four sides are equal and the diagonals are also equal then we can say it is a ___
a) Rhombus
b) Square
c) Trapezium
d) Rectangle
12. The distance between the points A(−6,7) and B(−1,−5) is ___
a) 13 cm
b) 12 cm
c) 11 cm
d) 10 cm
13. The distance between the points P(x,−1) and Q(3, 2) is 5. So the value of x is____
a) 3
b) −2
c) −1
d) 2
14. The point on the y axis which is equidistant from the point M(6, 5) and N(−4, 3) is ___
a) (0, 5)
b) (0, 3)
c) (3, 0)
d) (0,9)
15. The three vertices of a parallelogram taken in order are (−1, 0) (3, 1) and (2, 2) respectively. The co-ordinates of fourth vertex will be ___
a) (−3, 1)
b) (3, 1)
c) (−2, 1)
d) (2,−1)
16. The co-ordinates of the centroid of a triangle whose vertices are (0,6) (8,12) and (8,0) are ____
a) (16/3 , 6)
b) (11/3 , 5)
c) (2, 11/4)
d) (11/2 , 3/4)
17. The area of the triangle whose vertices are P(3, 2) Q(11, 8) R(8, 12) is___
a) 125 m2
b) 25 m2
c) 35 m2
d) 60 m2
18. Three points will be ___ if the area of the triangle formed by the given points is 0.
a) Collinear
b) Adjacent
c) Zero
d) Equal
19. If D,E,F are the mid points of sides BC, CA and AB respectively of ΔABC then area of ΔABC =___
a) 1/3
b) 1/2
c) 1/4
d) 1/5
20. The area of a triangle formed by (a, b+c) (b, c+a) (c, a+b) is ___
a) 0
b) (ab, ac)
c) (a + b + c)
d) (a + b −c)
21. The distance between the points (0, 5) and (−5, 0) is ____
(a) 5
(b) 5√2
(c) 2√5
(d) 10
22. The diagonals of a rhombus are ___
a) Perpendicular
b) Parallel
c) Adjacent
d) Similar
23. A line drawn from the vertex to the opposite side which cuts the
opposite side into to equal parts is called a ____
a) Altitude
b) Ray
c) Median
d) Angle
24. In the 4th quadrant for (x , y) we have ___
a) x > 0, y < 0
b) x > 0 , y > 0
c) x < 0 , y < 0
d) x < 0 , y > 0
25. AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and
B(5, 0). The length of its diagonal is ___
(a) 5
(b) 3
(c) √34
(d) 4
26. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is _____
(a) 5
(b) 12
(c) 11
(d) 7 + √5
27. If P (α, 4) is the mid-point of the line segment joining the
points Q(−6, 5) and R(−2, 3), then the value of α is__
(a) −4
(b) −12
(c) 12
(d) −6
28. If the distance between the points (4, P) and (1, 0) is 5, then the value of P is ___
(a) 4 only
(b) ± 4
(c) −4 only
(d) 0
29. If the points A(1, 2), O(0, 0), C(a, b) are collinear, then____
(a) a = b
(b) a = 2b
(c) 2a = b
(d) a = −b
30. The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is ____
(a) (a + b + c)²
(b) 0
(c) a + b + c
(d) abc
31. The distance between the points P (a, b) and Q (−a, −b) is_____
(a) (a + b )²
(b) 2 √a² + b²
(c) a + b
(d) 2 √abc
32. The coordinates of a point A where AB is the diameter of the circle whose centre is (2, −3) and B is (1,4) will be _____
(a) (−3, 10)
(b) (3, −10)
(c) (−2, 10)
(d) (2,−10)
33. The relation between x and y if the points (x, y) (1, 2)and (7, 0) are collinear will be ______
(a) x + 3y −7 = 0
(b) x + 3y −5 = 0
(c) x + 5y −7 = 0
(d) 2x + 3y −7 = 0
34. The distance of the point (3, −4) from the origin will be _____
(a) 5
(b) 3
(c) √3
(d) 4
35. If the line is trisected it means that the line is divided into ____exact parts
(a) One
(b) Two
(c) Three
(d) Four
Answers + Clues:
1: (a) ⇒ Use distance formula for each side and if all the four answers should be same.
2: (a) ⇒ Use distance formula and find value of x
3: (c) ⇒ Use mid point formula
4: (b) ⇒ Text book ( distance formula)
5: (b) ⇒ Use distance formula
6: (b) ⇒ Use mid point formula
7: (d) ⇒ Use section formula
8: (c) ⇒ Use section formula
9: (a) ⇒ Use mid point formula
10: (b) ⇒ Use section formula
11:(b) ⇒ Definition
12:(a) ⇒ Use distance formula
13:(c) ⇒ Use distance formula and PQ = 5
14:(d) ⇒ A point on the y axis is of the form(o,y) and the required point is R(o,y) and RM=RN.
15:(c) ⇒ Co-ordinates of mid point of AC= co-ordinates of mid point of BD.
16:(a) ⇒ Co-ordinates of centroid of a triangle whose angles are (a1,b1) (a2,b2) (a3,b3)
17:(a) ⇒ Use area of triangle formula
18:(a) ⇒ Formula
19:(c) ⇒ Area of triangle formula
20:(a) ⇒ Use area of triangle formula
21:(b) ⇒ Distance Formula
22:(a) ⇒ Property of rhombus
23:(c) ⇒ Definition of median
24:(d) ⇒ Quadrants property
25: (c) ⇒ Use Distance Formula and find the length of diagonal AB
26: (b) ⇒ Use Distance Formula and find the length of each side ,then add the three sides
27: (b) ⇒ Use Distance Formula and find PQ and PR.Then PQ = PR
28: (b) ⇒ Use distance formula
29: (c) ⇒ If the points are collinear then AO + OC = AC
30: (b) ⇒ Use area of triangle formula
31. (b) ⇒ Distance Formula
32. (b) ⇒ The centre of the circle bisects the diameter
33. (a) ⇒ Points will be collinear if area of ABC = 0
34. (a) ⇒ Use distance formula
35. (c) ⇒ Trisect means divide into 3 equal parts