Question

P(0,6) and Q(15,3) are the endpoints of a line segment what is the midpoint M of that line segment
Write the coordinates as decimals or integers

Answer 1

To find the midpoint \( M \) of a line segment with endpoints \( P(0, 6) \) and \( Q(15, 3) \), you can use the midpoint formula:

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

Where \( (x_1, y_1) \) are the coordinates of point \( P \) and \( (x_2, y_2) \) are the coordinates of point \( Q \).

For the given points:

- \( P(0, 6) \) means \( x_1 = 0 \) and \( y_1 = 6 \)
- \( Q(15, 3) \) means \( x_2 = 15 \) and \( y_2 = 3 \)

Now, substitute the values into the formula:

\[
M = \left( \frac{0 + 15}{2}, \frac{6 + 3}{2} \right)
\]

Calculating each component:

\[
M_x = \frac{0 + 15}{2} = \frac{15}{2} = 7.5
\]
\[
M_y = \frac{6 + 3}{2} = \frac{9}{2} = 4.5
\]

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

\[
M(7.5, 4.5)
\]