Question

Find the value of k, if the points P (5, 4), Q (7, k) and R (9, -2) are collinear.

• A. -1
• B. 1
• C. -8/3
• D. 3/4

Answer 1

The correct option is B

1

If area of triangle formed by these points is zero then the given points must lie in straight line.
Area of triangle $=\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$
$\frac{1}{2}\left[5\right(k+2)+7(-2-4)+9(4-k\left)\right]=0$
5k+10 -42 +36-9k=0
-4k +4=0
k=1