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.

$x=\frac{a}{a+b}(x_2-x_1_{})+x_1$

Replacing the coordinates, we have.

$x=\frac{1}{1+4}(12-4)+4=\frac{1}{5}(8)+4=\frac{8}{5}+4=\frac{8+20}{5}=\frac{28}{5}$

So, the x-coordinate is 28/5.

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

$y=\frac{a}{a+b}(y_2-y_1)+y_1$

Replacing the coordinates, we have.

$y=\frac{1}{1+4}(10-(-2))-2=\frac{1}{5}(10+2)-2=\frac{12}{5}-2=\frac{12-10}{5}=\frac{2}{5}$

So, the y-coordinate is 2/5.

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

The image below shows the point.