Question

33. If the points A(x,-11), B (5, y), C(2, 15) and D (1,1) are the vertices of a parallelogram ABCD, find the values
of x and y.
Ans: (4,3)
34. Three vertices of a parallelogram are (a, 2a + b), (-2a, b - a), (2a - b, - a). Find the fourth vertex.
Ans: (5a - b, 2a)
35. Find the third vertex of a triangle if its two vertices are (5,3) and (7,-3) and the midpoint of one side is (2, 2).
Ans: :(-1,1) or (-3,7)
36. Find the vertices of a triangle if the mid-points of its sides are (-1, -3), (2, 1), (4,5). Ans: (1,1), (-3,-7),(7,9)
37. Show that the points A(8, 10), B(5,7) and C(-1, 1) are collinear.
38. Find a relation between x and y if the points (x, y), (1, 2) and (7,0) are collinear. Ans: x + 3y = 7
39. Find the area of the triangle whose vertices are
(i) (8,-6), (-4, 6) and (-10,-8) (ii) (3, 2), (-1,0) and (1,-12) (iii) A(-5, 7), B(-4,-5) and C(4,5)
Ans: : (i) 120 sq.unit (ii)26 sq, (iii) 53 sq.
40. If the vertices of a triangle are pík, 2k), Q (-2, 6) and R (3, 1) and its area is 5 sq units, then find the value of k.
Ans: k=2 or 2/3
41. (i) For what value of m are the points (3,5), (m, 6) and (2 ) collinear? Ans: (i)m=2(i) p = 1
(ii) Find the value of p for which the points (-1,3), (2, p) and (5, -1) are collinear.
42. Find the values of k for which the points A(-5, 1), B(1,k) and C(4,-2) are collinear. Also find the ratio in
which B divides AC.
Ans: k = -1,2:1.
43. Find the distance between the points :
(i) P (-6, 7) and Q(-1,-5).
Ans: :13
(ii) Aſat, , 2at ) and B(at, 2at,).
Ans: a(tz - tı) (tz + tu)? +4
44. If the point (x, y) is equidistant from the points (a + b, b - a) and (a - b, a + b), prove that bx = ay.
45. Find the value of x, if the distance between the points (x,-1) and (3, 2) is 5. Ans: :x=7 or -1
Chou that the noints (a, al. (-a, -a) and - 3a, 3a ) are the vertices of an equilateral triangle.​

Answer 1

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