Find the coordinates of the midpoint of line PQ given P(-3, 4) and Q(5, 6).

Answer Details

The midpoint of a line segment is the point that is exactly halfway between two given points. To find the midpoint between two points, you use the midpoint formula:

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

Here, \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points.

For this problem:

• Point \( P \) has coordinates \( (-3, 4) \)
• Point \( Q \) has coordinates \( (5, 6) \)

Plugging these into the formula:

\[ \text{Midpoint} = \left( \frac{-3 + 5}{2},~~\frac{4 + 6}{2} \right) \]

Now, calculate each part:

• \( -3 + 5 = 2 \), so the x-coordinate is \( \frac{2}{2} = 1 \)
• \( 4 + 6 = 10 \), so the y-coordinate is \( \frac{10}{2} = 5 \)

Therefore, the midpoint is at \( (1, 5) \).

Why this works: The formula averages the x-values and y-values of the two endpoints, which guarantees you find the point exactly halfway between them on both the horizontal (x) and vertical (y) axes.