Question

PQ has endpoints at p(10,0) and Q(6,4) find the midpoint M of PQ
write the coordinates as decimals or integers
M=(__,__)

Answer 1

To find the midpoint \( M \) of the line segment \( PQ \) with endpoints \( P(10, 0) \) and \( Q(6, 4) \), 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 \( P \) and \( (x_2, y_2) \) are the coordinates of point \( Q \).

Substituting the coordinates of points \( P \) and \( Q \):

- \( x_1 = 10 \)
- \( y_1 = 0 \)
- \( x_2 = 6 \)
- \( y_2 = 4 \)

Now, calculating the coordinates of the midpoint \( M \):

\[
M_x = \frac{10 + 6}{2} = \frac{16}{2} = 8
\]

\[
M_y = \frac{0 + 4}{2} = \frac{4}{2} = 2
\]

So the coordinates of the midpoint \( M \) are:

\[
M = (8, 2)
\]

Thus, the final answer is:

\( M = (8, 2) \)