1. ## Math Question

This is a question on a math university quiz.

Find x and y such that the points A(-1,3), B(x,9) and C(5,y) are collinear with point B lying midway between points A and C.

Well first, I did B-C=C-A as they are collinear, and now I'm stuck. Can anyone tell me how to do this question

Thanks

2. Originally Posted by monkius
This is a question on a math university quiz.

Find x and y such that the points A(-1,3), B(x,9) and C(5,y) are collinear with point B lying midway between points A and C.

Well first, I did B-C=C-A as they are collinear, and now I'm stuck. Can anyone tell me how to do this question

Thanks
Hello monkius,

If B is to be the midpoint, we must use the midpoint formula to determine the values of x and y.

$\displaystyle Midpoint=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

Using points A and C, we substitute to get

$\displaystyle Midpoint=\left(\frac{5-1}{2}, \frac{y+3}{2}\right)$

Now, we know $\displaystyle \frac{5-1}{2}=x$

Therefore, x = 2.

We also know that $\displaystyle \frac{y+3}{2}=9$

Therefore, y = 15.

You can substitute these values back into points B and C to verify the slopes of AB, BC and AC are the same.