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)
Responses

(−6, 12)
(−6, 12)

(4, −2)
(4, −2)

(6, 6)
(6, 6)

(5, 2)

Answer 1

To find the ordered pair for point Y, we can use the midpoint formula, which states that the midpoint M of a line segment connecting points \( X(x_1, y_1) \) and \( Y(x_2, y_2) \) is given by:

\[
M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
\]

In this case, we know:

- Midpoint \( M = (2, 8) \)
- Point \( X = (10, 4) \)

Let point \( Y = (x_2, y_2) \). We can set up the equations based on the midpoint coordinates:

1. For the x-coordinates:
\[
\frac{10 + x_2}{2} = 2
\]

2. For the y-coordinates:
\[
\frac{4 + y_2}{2} = 8
\]

Now, we can solve these equations one by one.

Starting with the first equation:

\[
\frac{10 + x_2}{2} = 2
\]
Multiply both sides by 2:
\[
10 + x_2 = 4
\]
Now, subtract 10 from both sides:
\[
x_2 = 4 - 10 = -6
\]

Now, solving the second equation:

\[
\frac{4 + y_2}{2} = 8
\]
Multiply both sides by 2:
\[
4 + y_2 = 16
\]
Now, subtract 4 from both sides:
\[
y_2 = 16 - 4 = 12
\]

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

The ordered pair for point Y is \( \boxed{(-6, 12)} \).