Question

UV has endpoints at U(12,13) and V(-15,0) find the midpoint M of UV
Write the coordinates as decimals or integers
M =

Answer 1

To find the midpoint \( M \) of the segment \( UV \) with endpoints \( U(12, 13) \) and \( V(-15, 0) \), you can use the midpoint formula:

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

where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of points \( U \) and \( V \).

Substituting the coordinates of \( U \) and \( V \):

- \( x_1 = 12 \)
- \( y_1 = 13 \)
- \( x_2 = -15 \)
- \( y_2 = 0 \)

Now plug these values into the midpoint formula:

\[
M = \left( \frac{12 + (-15)}{2}, \frac{13 + 0}{2} \right)
\]

Calculating the x-coordinate:

\[
M_x = \frac{12 - 15}{2} = \frac{-3}{2} = -1.5
\]

Calculating the y-coordinate:

\[
M_y = \frac{13 + 0}{2} = \frac{13}{2} = 6.5
\]

Therefore, the coordinates of the midpoint \( M \) are:

\[
M = (-1.5, 6.5)
\]

So, the final answer is:

\[
M = (-1.5, 6.5)
\]