Question

the coordinates of points A and B are A(4,-2) and B(12,10). What are the coordinates of the point 1\4 of the way from A to B?

Answer 1

The given points are A(4, -2) and B(12, 10).

The given ratio is 1/4, where a = 1, and b = 4.

To find the x-coordinate, we use the following formula.

`x=(a)/(a+b)(x_2-x_1_{})+x_1`

Replacing the coordinates, we have.

`x=(1)/(1+4)(12-4)+4=(1)/(5)(8)+4=(8)/(5)+4=(8+20)/(5)=(28)/(5)`

So, the x-coordinate is 28/5.

To find y-coordinate, we use the following formula.

`y=(a)/(a+b)(y_2-y_1)+y_1`

Replacing the coordinates, we have.

`y=(1)/(1+4)(10-(-2))-2=(1)/(5)(10+2)-2=(12)/(5)-2=(12-10)/(5)=(2)/(5)`

So, the y-coordinate is 2/5.

Therefore, the point is (28/5, 2/5).

The image below shows the point.