Question

The co-ordinates of the point which divides the line joining the points (–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

The correct option is A

(1, 3)

If a point $P(x,y)$ divides a line segment joining $(x_1,y_1)\text{and}(x_2,y_2)$ in the ratio $m:n$, then by section formula, the coordinates of $P$ are:

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

Let $P(x,y)$ divide the line segment $AB$ joining $A(-1,7)$ and $B(4,-3)$ in the ratio $2:3$. Then by using section formula, the co-ordinates of $P$ are given by:

$(\frac{2\times 4+3\times (-1)}{2+3},\frac{2\times (-3)+3\times 7}{2+3})$
$=(\frac{8-3}{5},\frac{-6+21}{5})$
$=(\frac{5}{5},\frac{15}{5})$

Thus, the coordinates of $P$ are $(1,3).$