Question

If the midpoint of line segment is XY id at (2, 8) and point x id at (10, 4) what is the ordered pair of point y

Answer 1

To find the coordinates of point \( Y \) given the midpoint \( M \) of line segment \( XY \) and point \( X \), we can use the midpoint formula. The midpoint \( M \) of line segment \( XY \) is given by the formula:

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

where \( (x_1, y_1) \) are the coordinates of point \( X \) and \( (x_2, y_2) \) are the coordinates of point \( Y \).

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

We can set up the equations like this:

\[
\frac{10 + x_2}{2} = 2
\]

\[
\frac{4 + y_2}{2} = 8
\]

Now, let's solve for \( x_2 \) and \( y_2 \).

1. For \( x_2 \):

\[
\frac{10 + x_2}{2} = 2
\]

Multiply both sides by 2:

\[
10 + x_2 = 4
\]

Subtract 10 from both sides:

\[
x_2 = 4 - 10
\]

\[
x_2 = -6
\]

2. For \( y_2 \):

\[
\frac{4 + y_2}{2} = 8
\]

Multiply both sides by 2:

\[
4 + y_2 = 16
\]

Subtract 4 from both sides:

\[
y_2 = 16 - 4
\]

\[
y_2 = 12
\]

Thus, the coordinates of point \( Y \) are:

\[
Y = (-6, 12)
\]

The ordered pair of point \( Y \) is \( (-6, 12) \).