Question

If point Q is the midpoint of segment AM, find midpoint Q.
Points on the line segment are (5,2) and (-2,-3).

Answer 1

To find the midpoint \( Q \) of the segment defined by points \( A(5, 2) \) and \( M(-2, -3) \), we can use the midpoint formula. The midpoint \( Q(x, y) \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

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

In this case:

- \( A(5, 2) \) gives us \( x_1 = 5 \) and \( y_1 = 2 \)
- \( M(-2, -3) \) gives us \( x_2 = -2 \) and \( y_2 = -3 \)

Now, we substitute these values into the midpoint formula:

\[
Q(x, y) = \left( \frac{5 + (-2)}{2}, \frac{2 + (-3)}{2} \right)
\]

Calculating each component:

1. For the x-coordinate:

\[
\frac{5 + (-2)}{2} = \frac{5 - 2}{2} = \frac{3}{2} = 1.5
\]

2. For the y-coordinate:

\[
\frac{2 + (-3)}{2} = \frac{2 - 3}{2} = \frac{-1}{2} = -0.5
\]

Thus, the midpoint \( Q \) is:

\[
Q\left(1.5, -0.5\right)
\]

Therefore, the coordinates of the midpoint \( Q \) are \( \left( \frac{3}{2}, -\frac{1}{2} \right) \) or \( (1.5, -0.5) \).