Q1.
Two vertices of a triangle are (4,2) (9,5) and its centroid is at the origin, find the co-ordinate of the third vertex.
(a) (13,0) (b) (-13,-7) (c) (13,7) (d) (20,7)
Solution.
(b) (-13,-7)
Let third coordinate is (x,y)
(4 + 9 + 2)/3 = 0
13 + x = 0
x = -13
(2 + 5 + y)/3 = 0
7 + y = 0
y = -7
Solution
Q2.
G be the centroid of a triangle ABC, then AB2 + BC2 + CA2 = _____________.
(a) 3(GA2 + GB2 + GC2) (b) 2(GA2 + GB2 +GC2)
(c) 4(GA2 + GB2 + GC2) (d) None of these
Solution.
(a) 3(GA2 + GB2 + GC2)
Solution
Q3.
Find the area of triangle, if points are ,(a, b + c )(b,c + a)(c,a + b)
(a) 0 sq units(points are collinear)
(b) 2 sq unit (c) 3 sq unit (d) 19 sq unit
Solution.
(a) 0 sq units(points are collinear)
Solution
Q4.
If P(x,y) is any point on the line joining the points A(a,o) and B(o,b), then x/a + y/b = __________.
(a) 4 (b) 1 (c) 2 (d) 3
Solution.
(b) 1
Solution
Q5.
Find the value of k, if the points A(3,-4) B(8,1) and C(2,k) are collinear if 1/a + 1/b = __________
(a) 3 (b) 2
(c) 5 (d) -5
Solution.
(d) -5
Solution
Q6.
The points (a,0),(0,b) and (1,1) are collinear if 1/a + 1/b = ______.
(a) 1 (b) 2 (c) 3 (d) 4
Solution.
(a) 1
Solution
Q7.
Find the distance between the points (sinθ , cosθ) and (cosθ , sinθ)
(a) 2 (b) 1 (c) √2 (d) √3
Solution.
d = √(sinθ - cosθ)2 + (-cosθ - sinθ)2
= √sin2θ + cos2θ - 2sinθcosθ + cos2θ + sin2θ +
2sinθcosθ
= √2
Solution
Q8.
Find the distance between the points P(a tan45o , 0) and Q(1 - sin900 , 0).
(a) a + 2 (b) a (c) a2
(d) 2a
Solution.
P(a tan45o = P(a,0)
Q(1 - sin900 , 0) = Q(1 - 1 ,0) = Q(0,0)
PQ = √ (a - 0)2 + (0 - 0)2 = √a2 = a
Solution
Q9.
Find the distance between the points (a2cos650 , 0)(0 , a2cos250).
(a) a4 (b) 2a (c) a (d) a2
Solution.
(d) a2
Solution
Q10.
The perimeter of the triangle formed by the points (0,0)(2,0)(0,2) is
(a) 2(2 + √2) (b) 2 (c) 2 + √2
(d) 4 + √2
Solution.
(a) 2(2 + √2)
Solution
