Question

The line joining the points $(2,3)$ and $(3,-1)$ passes through the point $(5,-9)$.

• A. False
• B. True

Answer 1

The correct option is B

True

Equation of the line through $(2,3)$ and $(3,-1)$ is given by,

Slope = $\frac{3-(-1)}{2-3}=\frac{4}{-1}=-4$

$⟹y-3=-4(x-2)$

$⟹y-3=-4x+8$

$⟹y+4x=11$

If $(5,-9)$ lies on the above line, then the points will satisfy the equation , hence substituting the value of x and y ( 5,9) in y + 4x , we have

L.H.S. = -9+4(5) = -9+20 = 11 = R.H.S.

Hence the line passes through $(5,-9)$.