Question

The points $(1,1),(-5,5)$ and $(13,\lambda )$ lie on the same straight line if $\lambda$ is equal to

• A. $7$
• B. $-7$
• C. $\pm 7$
• D. $0$

Answer 1

The correct option is B

$-7$

Compute the required value:

Let $A(1,1),B(-5,5)$ and $C(13,\lambda )$ are the points.

Slope of AB$=\frac{(5-1)}{(-5-1)}$

$\Rightarrow$ $=-\frac{4}{6}$

$\Rightarrow$ $=-\frac{2}{3}$

Slope of BC $=\frac{\lambda -5}{13+5}$

$\Rightarrow$ $=\frac{\lambda -5}{18}$

Since, if the points lie on the same straight line, the slopes will be equal.

$-\frac{2}{3}=\frac{(\lambda -5)}{18}$

$\Rightarrow$$\lambda -5=-12$

$\Rightarrow$ $\lambda =-12+5$

$\Rightarrow$ $\lambda =-7$

Hence option $\left(B\right)$ is the correct answer.