Question

Find the point, M, that divides segment AB into a ratio of 3.1 if A is at (-4,-2) and B is at (4. -10).

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Answer 1

The coordinates of M are (2,-8)

Explanation:

The coordinates of the point that divides the line segment joining

`A(x_1,y_1)` to
`B(x_2,y_2)` in the ratio m:n is given by:

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

If A is at (-4,-2) and B is at (4. -10) and the ratio is 3:1.

Then

`((3(4)+1(-4))/(3+1),(3(-10)+1(-2))/(3+1))`

`((8)/(4),(-32)/(4))`

The coordinates of M are (2,-8)