Question

(i) Find the coordinates of the point which divies the join of A(-1, 7) and B(4, -3) in the ratio 2 : 3.

(ii) Find the coordinates of the point which divides the join of A (-5, 11) and B(4, -7) in the ratio 7 : 2.

Answer 1

(i)The endpoints of AB are A $(-1,7)$ and B $(4,-3)$

Therefore, $(x_1=-1,y_1=7)$ and $(x_2=4,y_2=-3)$

Also, $m=2$ and $n=3$

Let the required point be $P(x,y)$

By section formula, we get

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

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

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

$y=\frac{(2\times -3)+(3\times 7)}{2+3}$

⇒$x=\frac{8-3}{5},y=\frac{-6+21}{5}$

⇒$x=\frac{5}{5},y=\frac{15}{5}$

Therefore, x = 1 and y = 3

Hence, the coordinates of the required point are (1,3)

(ii)The endpoints of AB are A $(-5,11)$ and B $(4,-7)$

Therefore, $(x_1=-5,y_1=11)$ and $(x_2=4,y_2=-7)$

Also, $m=7$ and $n=2$

Let the required point be $P(x,y)$

By section formula, we get

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

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

⇒ $x=\frac{(7\times 4)+(2\times -5)}{7+2},$

$y=\frac{(7\times -7)+(2\times 11)}{7+2}$

⇒$x=\frac{28-10}{9},y=\frac{49+22}{9}$

⇒$x=\frac{18}{9},y=\frac{-27}{9}$

Therefore, x = 2 and y = -3

Hence, the coordinates of the required point are (2,-3)