Question

A straight line passes through the points $A(2,-4)$ and $B(5,-2)$.
Find the value of $k$, if $AB$ passes through the point $P(k+3,k-4)$.

• A. $-25$
• B. $-28$
• C. $2$
• D. $-1$

Answer 1

Answer: (C)

$2$

Slope of Line AB $=\frac{-2-(-4)}{5-2}=\frac{2}{3}$

Equation of Straight line Will be $y+2=\frac{2}{3}(x-5)\Rightarrow 3y+6=2x-10\Rightarrow 2x-3y-16=0$

When this passes through point $P$

$2(k+3)-3(k-4)-16=0\Rightarrow 2k+6-3k+12-16=0\Rightarrow k=2$