Question

KL has endpoints at K(72,90) and L(97,16) find the midpoint M of KL
write the coordinates as decimals or integers

Answer 1

To find the midpoint \( M \) of the line segment \( KL \) with endpoints \( K(72, 90) \) and \( L(97, 16) \), we use the midpoint formula:

\[
M\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
\]

where \( (x_1, y_1) \) are the coordinates of point \( K \) and \( (x_2, y_2) \) are the coordinates of point \( L \).

Substituting in the values:

- \( x_1 = 72 \)
- \( y_1 = 90 \)
- \( x_2 = 97 \)
- \( y_2 = 16 \)

Now, calculate the midpoint:

\[
M\left(\frac{72 + 97}{2}, \frac{90 + 16}{2}\right) = M\left(\frac{169}{2}, \frac{106}{2}\right) = M(84.5, 53)
\]

Thus, the coordinates of the midpoint \( M \) are \( M(84.5, 53) \).