Question

BC has endpoints B(5,9) and C(-4,-5)find the coordinates of the midpointBC

Answer 1

We can find the midpoint of any line segment using the midpoint formula: M=(x1+x2/2,y1+y2/2). Essentially, the midpoint formula finds the average of two points. If we use B and the first point and C as the second, when we plug in our values we would have M=(5-4/2,9-5/2). This can be simplified to M=(1/2,4/2) or M=(1/2,2) which is the final answer.

I hope this helps.

Answer 2

Let's mark our midpoint with letter $M$. Here is the formula for finding it:
$M(x_{m},y_{m})=M( \frac{x_{b}+x_{a}}{2}, \frac{y_{b}+y_{a}}{2} )$

Now let's replace formula variables with corresponding values and calculate our midpoint:
$M(x_{m},y_{m})=M( \frac{5+(-4)}{2}, \frac{9+(-5)}{2} )=M( \frac{5-4}{2}, \frac{9-5}{2} )=$
$=M( \frac{1}{2}, \frac{4}{2} )=M(0.5,2)$

So midpoint of $BC$ is $M(0.5,2)$.