Question

find the value of k for which the point with coordinates (3, 2),(4, K) and (5, 3) are collinear

Answer 1

(3, 2) , (4, k) and (5,3) are collinear .
hence, area of triangle form by these points = 0
but we know,
area of triangle = 1/2[x1(y2-y3) + x2(y3-y1) + x3(y1 - y2)}
so, 0 = 1/2 [ 3(k - 3) + 4 (3 - 2) + 5(2 - k)]
0 = 3k - 9 + 4 + 10 - 5k
0 = -2k + 5
k = 5/2