Answer:
P₂ = (2, 1).
Explanation:
To find the coordinates of P₂, we can use the formula for the midpoint of a line segment, which is M = (x₁ + x₂)/2, (y₁ + y₂)/2, where M is the midpoint and (x₁, y₁) and (x₂, y₂) are the endpoints. Since we are given that M = (−3, 1) and P₁ = (−8, 1), we can substitute these values into the formula and solve for x₂ and y₂. We get
(−3, 1) = (−8 + x₂)/2, (1 + y₂)/2
Multiplying both sides by 2, we get
(−6, 2) = (−8 + x₂), (1 + y₂)
Equating the corresponding coordinates, we get
−6 = −8 + x₂
2 = 1 + y₂
Solving for x₂ and y₂, we get
x₂ = −6 + 8 = 2
y₂ = 2 − 1 = 1
Therefore, P₂ = (2, 1).