Find the value of $K$ for which the points $(7, - 2), (5, 1)$ and $(3, K)$ are collinear.

Open in App

Solution

If the points are collinear then the area of triangle will be O.
$Δ = \frac{1}{2} | x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) |$
$\Rightarrow | 7 (1 - k) + 5 (k + 2) + 3 (- 2 - 1) | = 0$
$\Rightarrow | 7 - 7 k + 5 k + 10 - 9 | = 0$
$\Rightarrow | - 2 k + 8 | = 0$
$\Rightarrow - 2 k = - 8$ so $k = 4$

Suggest Corrections

Similar questions

Find the value (s) of k for which the points $(3 k - 1, k - 2)$ , $(k, k - 7)$ and $(k - 1, - k - 2)$ are collinear.

^{'} K^{'}

(7, - 2) (5, 1) (3, K)

^{'} k^{'}

(7, - 2), (5, 1), (3, k)

Join BYJU'S Learning Program