Point P(−2, 5) is the midpoint of line segment AB. The coordinates of A are (−5, y) and the coordinates of B are (x, 3). Using the midpoint formula in coordinate geometry, what is the value of x, the x-coordinate of point B?

Introduction / Context:
This coordinate geometry question checks understanding of the midpoint formula for a line segment in the Cartesian plane. When the midpoint and one endpoint are known, we can use the midpoint relations to find the remaining coordinates of the other endpoint. Here we focus on determining the x-coordinate of point B.

Given Data / Assumptions:

• Midpoint P has coordinates (−2, 5).
• Endpoint A has coordinates (−5, y).
• Endpoint B has coordinates (x, 3).
• We need to find the value of x.
• The midpoint formula for endpoints (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂) / 2, (y₁ + y₂) / 2).

Concept / Approach:
The midpoint formula equates the average of the x-coordinates of the endpoints to the x-coordinate of the midpoint, and similarly for y. Since P is given as the midpoint, we can write two equations, one for x-coordinates and one for y-coordinates. To find x, we only need the x-coordinate relation, which involves A and B and the midpoint. Solving this linear equation provides the required x value.

Step-by-Step Solution:
Use the midpoint formula for x-coordinates: (x₁ + x₂) / 2 = x-coordinate of midpoint.Here, x₁ = −5 (from A), x₂ = x (from B), and the midpoint x-coordinate is −2.So, (−5 + x) / 2 = −2.Multiply both sides by 2: −5 + x = −4.Add 5 to both sides: x = −4 + 5.Therefore x = 1.

Verification / Alternative check:
With x = 1, the x-coordinates of A and B are −5 and 1. Their average is (−5 + 1) / 2 = −4 / 2 = −2, which matches the midpoint x-coordinate. Although the y-value was not required, we could also set up the y-coordinate equation to find y if needed. The consistency of the x-coordinate confirms that x = 1 is correct.

Why Other Options Are Wrong:
Substituting −1, 2, −2, or 0 in place of x does not produce a midpoint x-coordinate of −2 when combined with −5. For example, if x = 0, the average would be (−5 + 0) / 2 = −2.5, which is incorrect. Only x = 1 gives the correct midpoint coordinate.

Common Pitfalls:
Students sometimes forget to multiply both sides of the midpoint equation by 2, or they may incorrectly handle negative signs while adding −5 and x. Another mistake is to confuse the midpoint formula with the distance formula. Writing the equation clearly and double checking sign operations helps prevent these errors.

Final Answer:
The x-coordinate of point B is 1.