Question

The co-ordinates of the point which divides the join of $(–1,7)$ and $(4,–3)$ in the ratio $2:3$ is

• A. (1, 3)
• B. (-1, 3)
• C. (1,-3)
• D. (-1,-3)

Answer 1

Answer: (A)

Let $P(x,y)$ divides the line segment $AB$ joining the points $A(-1,7)$ and $B(4,-3)$ in the ratio $2:3$.

Recall the section formula, if a point $P(x,y)$ divides a line segment in the ratio $m:n$ at end points $(x_1,y_1)$ and $(x_2,y_2)$ then the coordinates of point,

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

Then by using section formula, the coordinates of $P$ are given by:

$P=(\frac{2\times 4+3\times (-1)}{2+3},\frac{2\times (-3)+3\times 7}{2+3})$

$=(\frac{8-3}{5},\frac{-6+21}{5})$

$=(\frac{5}{5},\frac{15}{5})$
$=(1,3)$

Therefore, The coordinates of the point are $(1,3)$.

Hence, Option $A$ is correct.