Question

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)
• (5, 2)
• (-6, 12)
• (4, - 2)
• (6, 6)

Answer 1

To find the coordinates of point Y, we can use the formula for the midpoint of a line segment. The coordinates of the midpoint M (xₘ, yₘ) of a segment connecting points X (x₁, y₁) and Y (x₂, y₂) are given by:

\[
xₘ = \frac{x₁ + x₂}{2}
\]
\[
yₘ = \frac{y₁ + y₂}{2}
\]

We know the midpoint M is at (2, 8), and point X is at (10, 4). Let point Y be (x₂, y₂).

Using the midpoint formula for the x-coordinates:

\[
2 = \frac{10 + x₂}{2}
\]

Multiplying both sides by 2:

\[
4 = 10 + x₂
\]

Subtracting 10 from both sides:

\[
x₂ = 4 - 10 = -6
\]

Now, using the midpoint formula for the y-coordinates:

\[
8 = \frac{4 + y₂}{2}
\]

Multiplying both sides by 2:

\[
16 = 4 + y₂
\]

Subtracting 4 from both sides:

\[
y₂ = 16 - 4 = 12
\]

Thus, point Y is at (-6, 12).

The ordered pair of point Y is:

\[
\boxed{(-6, 12)}
\]