To find the midpoint of the segment [tex]\( PQ \)[/tex] where [tex]\( P = (3, 1) \)[/tex] and [tex]\( Q = (-3, -7) \)[/tex], we use the midpoint formula. The midpoint [tex]\( M(x, y) \)[/tex] of a segment with endpoints [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] is given by:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Here, the coordinates of point [tex]\( P \)[/tex] are [tex]\( (3, 1) \)[/tex] and the coordinates of point [tex]\( Q \)[/tex] are [tex]\( (-3, -7) \)[/tex].
Let's break down the steps to find the midpoint:
1. Identify the coordinates of the endpoints:
- Point [tex]\( P \)[/tex]: [tex]\( x_1 = 3 \)[/tex], [tex]\( y_1 = 1 \)[/tex]
- Point [tex]\( Q \)[/tex]: [tex]\( x_2 = -3 \)[/tex], [tex]\( y_2 = -7 \)[/tex]
2. Apply the midpoint formula:
- Calculate the x-coordinate of the midpoint:
[tex]\[
x = \frac{x_1 + x_2}{2} = \frac{3 + (-3)}{2} = \frac{0}{2} = 0.0
\][/tex]
- Calculate the y-coordinate of the midpoint:
[tex]\[
y = \frac{y_1 + y_2}{2} = \frac{1 + (-7)}{2} = \frac{1 - 7}{2} = \frac{-6}{2} = -3.0
\][/tex]
3. Write the coordinates of the midpoint:
- The midpoint [tex]\( M \)[/tex] is [tex]\( (0.0, -3.0) \)[/tex].
So, the midpoint of segment [tex]\( PQ \)[/tex] is [tex]\( \left( 0.0, -3.0 \right) \)[/tex].
