Question

In what ratio is the line joining the points $A(4,4)$ and $B(7,7)$ divided by $P(-1,-1)$?

• A. $8:3$
• B. $5:8$
• C. $5:7$
• D. $7:4$

Answer 1

The correct option is B $5:8$

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

Let the point $(-1,-1)$ divide the line joining AB in the ratio $(n:m)$. It is clear that $(-1,-1)$ divides the line segment externally.

Then application of section formula gives us,
$(-1,-1)=[\frac{m\left(4\right)-n\left(7\right)}{m-n},\frac{m\left(4\right)-n\left(7\right)}{m-n}]$.

Comparison of the x-coordinates give us,

$-1=\frac{4m-7n}{m-n}$ or $-m+n=4m-7n$

Or $5m=8n$ or $\frac{n}{m}=\frac{5}{8}$.