WAEC 2021 Mathematics · Question 43

$\overline{XY}$ is a line segments with the coordinates X (- 8,- 12) and Y(p,q). if the midpoint of $\overline{XY}$ is (-4,-2) find the coordinates of Y.

Options

A.(-6,-2)
B.(0,8)
C.(4,10)
D.(0,4)

Answer: B. (0,8)

Explanation written with AI and checked against the answer key

Analyze the question: We are given one endpoint X(-8, -12) and the midpoint M(-4, -2) of line XY. We need to find the other endpoint Y(p, q). Concept: The midpoint formula is M = ((x₁ + x₂)/2, (y₁ + y₂)/2) Solution: For the x-coordinate: (-8 + p)/2 = -4 -8 + p = -8 p = 0 For the y-coordinate: (-12 + q)/2 = -2 -12 + q = -4 q = 8 So Y = (0, 8). Check: Midpoint of (-8, -12) and (0, 8) = (-8/2, -4/2) = (-4, -2). ✓ Answer: Option B (0, 8). Tip: A quick shortcut is Y = 2M − X. Double the midpoint, then subtract the known endpoint: 2(-4) − (-8) = 0 and 2(-2) − (-12) = 8. Always verify by plugging your answer back into the midpoint formula.

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XY‾\overline{XY}XY is a line segments with the coordinates X (- 8,- 12) and Y(p,q). if the midpoint of XY‾\overline{XY}XY is (-4,-2) find the coordinates of Y.

Options

Answer: B. (0,8)

$\overline{XY}$ is a line segments with the coordinates X (- 8,- 12) and Y(p,q). if the midpoint of $\overline{XY}$ is (-4,-2) find the coordinates of Y.