Question

A straight line passes through the points $(2,4)$ and $(5,-2)$. Taking $1cm=1$ units, mark these points on a graph paper and draw the straight line through these points. If points $(m,-4)$ and $(3,n)$ lie on the drawn line, find the values of $m$ and $n$.

• A. $m=1$ and $n=2$
• B. $m=3$ and $n=2$
• C. $m=6$ and $n=2$
• D. $m=9$ and $n=2$

Answer 1

The correct option is C $m=6$ and $n=2$

Equation of a straight line passing through$(x_1,y_1)$ and $(x_2,y_2)$ is

$[y-y_1$=$\frac{y_2-y_1}{x_2-x_1}(x-x_1)]$

here $(x_1,y_1)$=$(2,4)$ and $(x_2,y_2)=(5,-2)$

$y-4$=$\frac{-2-4}{5-2}(x-2)$

$3y-12=-6x+12$

$6x+3y=24$

$(m,-4)$ and $(3,n)$ lie on the line then,

$6m-12=24$

$6m=36$

$m=6$

$18+3m=24$

$3m=6$

$n=2$

Therefore $m=6$ and $n=2$