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

Analysis

To find the midpoint of a line segment joining two points $P(x_1, y_1)$ and $Q(x_2, y_2)$, we use the midpoint formula. This formula calculates the average of the x-coordinates and the average of the y-coordinates.

Concept

The midpoint $M(x, y)$ of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

Solution

Given the points $P(-3, 4)$ and $Q(5, 6)$:

• $x_1 = -3, y_1 = 4$
• $x_2 = 5, y_2 = 6$

Step 1: Calculate the x-coordinate of the midpoint

Step 2: Calculate the y-coordinate of the midpoint

Step 3: Combine the coordinates The midpoint is $(1, 5)$.

Comparing this result to the given options, it matches option D.

Exam Tip

When dealing with midpoint or gradient questions, always label your coordinates $(x_1, y_1)$ and $(x_2, y_2)$ clearly before you start. This simple habit prevents "sign errors" (like mixing up a negative sign), which is the most common reason students lose marks in coordinate geometry.