Question

What are the coordinates of the point 3/4 of the way from A to B?

Answer 1

(-3.5, 1.25)

Explanation:

Given:

A(-5, -4)

B(-3, 3)

Required:

Coordinates of the point 3/4 of the distance between A and B.

SOLUTION:

Find the coordinates using the formula below:

`(x, y) = (x_1 + k(x_2 - x_1), y_1 + k(y_2 - y_1))`

Let,

`A(-5, -4) = (x_1, y_1)`

`B(-3, 3) = (x_2, y_2)`

`k = (3)/(4)`

Plug in the values into the formula:

`(x, y) = (-5 + (3)/(4)(-3 -(-5)), -4 + (3)/(4)(3 -(-4))`

`(x, y) = (-5 + (3)/(4)(2), -4 + (3)/(4)(7)`

`(x, y) = (-5 + (3*2)/(4), -4 + (3*7)/(4)`

`(x, y) = (-5 + 1.5, -4 + 5.25)`

`(x, y) = (-3.5, 1.25)`

The coordinates of the point 3/4 from A to B are (-3.5, 1.25).