Question

In the coordinate plane shown point not shown) lies on segment AB. Vf the ratioof the length of segment AC to the length of segment CB is 3:1, what is the y-coordinate of point C. Round to the nearest tenth.

Answer 1

We know that the point C lies in the segment AB. Since the ratio between AC and CB is 3:1, we also know it lives in the first 1/4 of the segment.

To calculate the point at 1/4 of the segment, we can find the midpoint, and then the midpoint of the segment made with point A and the midpoint.

The midpoint y-coordinate is given by:

$\frac{y_1+y_2}{2}=\frac{4+10}{2}=7$

Now, calculating the midpoint between the midpoint of the segment AC and A, we have:

$\frac{4+7}{2}=\frac{11}{2}=5.5$

And this is our answer. The y coordinate of the point C is 5.5