If the midpoint of line segment XY is at (2, 8) and point X is at (10, 4) , what is the ordered pair of point Y?(1 point) Responses (5, 2) (5, 2) (4, −2) (4, −2) (−6, 12) (−6, 12) (6, 6)
To find the coordinates of point Y, we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint ((a, b)) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by:
a = (x₁ + x₂)/2
b = (y₁ + y₂)/2
In this case, we are given that the midpoint of line segment XY is at (2, 8) and point X is at (10, 4).
Let's use the midpoint formula to find the coordinates of point Y.
For the x-coordinate:
a = (x₁ + x₂)/2
2 = (10 + x₂)/2
4 = 10 + x₂
x₂ = 4 - 10
x₂ = -6
For the y-coordinate:
b = (y₁ + y₂)/2
8 = (4 + y₂)/2
16 = 4 + y₂
y₂ = 16 - 4
y₂ = 12
Therefore, the ordered pair of point Y is (-6, 12).