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

`M(-2,-3)`

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=(mx_2+nx_1)/(m+n),y=(my_2+ny_1)/(m+n)]`

`[x=(5\cdot -1+1\cdot -7)/(5+1),y=(5\cdot -4+1\cdot 2)/(5+1)]`

`[x=(-5-7)/(6),y=(-20+2)/(6)]`

`[x=(-12)/(6),y=(-18)/(6)]`

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

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