Question

Find the coordinates of the point 7/10

of the way from A to B.

A(-4,-7)
B(12,4)

Answer 1

C(7.2,0.7)

Explanation:

Let point C be
`(7)/(10)` of the way from A to B, then
`AC:CB=7:3.`

If point
`C(x_C,y_C)` divides segment AB with endpoints
`A(x_A,y_A),\ B(x_B,y_B)` in the ratio
`m:n,` then

`x_C=(nx_A+mx_B)/(m+n)\\ \\y_C=(ny_A+my_B)/(m+n)`

In your case, A(-4,-7) and B(12,4), so

`x_C=(3\cdot (-4)+7\cdot 12)/(7+3)=(-12+84)/(10)=7.2\\ \\y_C=(3\cdot (-7)+7\cdot 4)/(7+3)=(-21+28)/(10)=0.7`