Question

Point a is at -2,4 and point c is at 4,7. Find the coordinates of point b on ac such that the ratio is 1:3

Answer 1

We have been given that point a is at $(-2,4)$ and point c is at $(4,7)$. We are asked to find the coordinates of point b on segment ac such that the ratio is 1:3.

We will use section formula to solve our given problem.

When point P divides a segment internally in the ratio m:n, the coordinates of point P would be:

$[x=\frac{mx_2+nx_1}{m+n}, y=\frac{my_2+ny_1}{m+n}]$

Let point $(-2,4)=(x_1,y_1)$ and point $(4,7)=(x_2,y_2)$.

$[x=\frac{1(4)+3(-2)}{1+3}, y=\frac{1(7)+3(4)}{1+3}]$

$[x=\frac{4-6}{4}, y=\frac{7+12}{4}]$

$[x=\frac{-2}{4}, y=\frac{19}{4}]$

$[x=-0.5, y=4.75]$

Therefore, the coordinates of point 'b' would be $(-0.5,4.75)$.