Question

Quadrilateral JKLM has vertices J(–7, –2), K(–2, –2), L(–3, –4), and M(–6, –4). Find the midpoints of each of the sides JM andKL.

Answer 1

To find the midpoint of a segment (or the midpoint between two points - here the endpoints of the side) we use the midpoint formula. What it comes down to is finding the "average" of the x-coordinate and the "average" of the y-coordinate.

The formula is as follows. The midpoint of the segment with endpoints $(x_{1} ,y_{1})$ and $(x_{2} ,y_{2})$ is given by $( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Let us find the midpoint of side JM. It does not matter which point we designate with the 1s and which we designate with the 2s so let's let J (-7,2) = $(x_{1} ,y_{1})$ and M (-6,-4) = $(x_{2} ,y_{2})$.

Now we plug these into the formula as follows: $( \frac{-7+-6}{2},\frac{-2+-4}{2}) = ( \frac{-13}{2},\frac{-6}{2})=(-6.5,-3)$

Let us now find the midpoint of side KL. It does not matter which point we designate with the 1s and which we designate with the 2s so let's let K (-2,-2) = $(x_{1} ,y_{1})$ and L (-3,-4) = $(x_{2} ,y_{2})$

Now we plug these into the formula as follows: $( \frac{-2+-3}{2},\frac{-2+-4}{2}) = ( \frac{-5}{2},\frac{-6}{2})=(-2.5,-3)$

Answer 2

We calculate the midpoint by taking the average of the x- and y-coordinates of both points. For side JM, with point J(-7, -2) and point M(-6, -4), we average the x-coordinates to get (-7 - 6) / 2= -13/2, and the y-coordinates average to (-2 - 4) / 2 = -3. So the midpoint of side JM is (-13/2, -3).
The calculation is similar for side KL: (-2 - 3) / 2 = -5/2, and (-2 - 4) / 2 = -3, so the midpoint of side KL is (-5/2, -3).