Question

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The midpoint of the line segment from P₁ to P₂ is (-4,2). If P₁ = (-6,3), what is P2?
P₂ = (Type an ordered pair.)

Answer 1

(- 2, 1)

Explanation:

Let the midpoint of P₁ P₂ be M (x, y)

If (x₁, y₁) and (x₂, y₂) be the coordinates of P₁ and P₂ respectively,
x = (x₁ + x₂)/2

Therefore
2x = x₁ + x₂
x₂ = 2x - x₁

Given (x, y), midpoint is (-4, 2) and P₁ is(-6, 3)
x₂ = 2(-4) - (-6) = -8 + 6 = -2

Similarly
y₂ = 2y - y₁
y₂ = 2(2) - 3 = 4 - 3 = 1

Therefore coordinates of P₂ are (-2, 1)