Question

Find the point, M, that is five-sixths of the distance from A(-7, 2) to B(-1, -4)

Answer 1

M(-7+(6*5/6),2-(6*5/6))
M(-2,-3)

Answer 2

Answer:

$M(-2,-3)$

Step-by-step explanation:

We are asked to find the coordinates of point M, that is five-sixths of the distance from A(-7, 2) to B(-1, -4).

Since M is five-sixths of the distance from A to B, so it will divide A to B in ratio 5: 1.

Use section formula:

When a point P divides segment AB internally in ratio m:n, then coordinates of point P are:

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

$[x=\frac{5\cdot -1+1\cdot -7}{5+1},y=\frac{5\cdot -4+1\cdot 2}{5+1}]$

$[x=\frac{-5-7}{6},y=\frac{-20+2}{6}]$

$[x=\frac{-12}{6},y=\frac{-18}{6}]$

$[x=-2,y=-3]$

Therefore, the coordinates of point M would be $(-2,-3)$.