Question

Point A has coordinates (7,2). Point B has coordinates (2,-10). Find the coordinates of point P that partition AB in the ratio of 5:1

Answer 1

Answer:

$(\frac{17}{6},-8)$.

Step-by-step explanation:

We have been given that point A has coordinates (7,2). Point B has coordinates (2,-10). We are asked to find the coordinates of point P that partition AB in the ratio of 5:1.

We will use segment formula to solve our given problem.

When a point M divides a segment internally in ratio m:n, the coordinates of point M are:

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

$[x=\frac{5*2+1*7}{5+1},y=\frac{5*(-10)+1*2}{5+1}]$

$[x=\frac{10+7}{6},y=\frac{-50+2}{6}]$

$[x=\frac{17}{6},y=\frac{-48}{6}]$

$[x=\frac{17}{6},y=-8]$

Therefore, the coordinates of point P would be $(\frac{17}{6},-8)$.