The midpoint of P(x, y) and Q(8, 6) is (5, 8). Find x and y.

Analysis

To find the coordinates of a point given the midpoint of a line segment, we use the Midpoint Formula. The midpoint $M(x_m, y_m)$ of a line segment connecting two points $P(x_1, y_1)$ and $Q(x_2, y_2)$ is calculated as:

Concept

In this problem, we are given:

• Point $P = (x, y)$
• Point $Q = (8, 6)$
• Midpoint $M = (5, 8)$

We need to substitute these values into the midpoint formula to solve for the unknown variables $x$ and $y$.

Step-by-Step Solution

Step 1: Solve for $x$ Using the formula for the x-coordinate:

Multiply both sides by 2:

Subtract 8 from both sides:

Step 2: Solve for $y$ Using the formula for the y-coordinate:

Multiply both sides by 2:

Subtract 6 from both sides:

Step 3: Combine the results The coordinates of point $P$ are $(x, y) = (2, 10)$.

Conclusion

Comparing our result $(2, 10)$ with the given options, it matches option A.

Exam Tip

When dealing with midpoint questions, you can always verify your answer by calculating the average of your result and the given point. If the average equals the midpoint provided in the question, your answer is definitely correct!