Question

The coordinates of point J are (-7,2), and the midpoint of line segment JK is at L(3,5)
What are the coordinates of point K?

A. (13,8)
B. (4,-2)
C. (-1,12)
D. (8,3)

Answer 1

To find the coordinates of point K, we can use the midpoint formula. The midpoint \( L \) of a line segment \( JK \) with endpoints \( J(x_1, y_1) \) and \( K(x_2, y_2) \) is given by:

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

Given:
- The coordinates of point J are \( J(-7, 2) \).
- The coordinates of the midpoint L are \( L(3, 5) \).

We can set up the equations for the midpoint based on these coordinates:

\[
\left( \frac{-7 + x_2}{2}, \frac{2 + y_2}{2} \right) = (3, 5)
\]

This gives us two equations:

1. \[
\frac{-7 + x_2}{2} = 3
\]
2. \[
\frac{2 + y_2}{2} = 5
\]

Now, solve each equation for \( x_2 \) and \( y_2 \):

1. Multiply both sides of the first equation by 2:
\[
-7 + x_2 = 6 \implies x_2 = 6 + 7 \implies x_2 = 13
\]

2. Multiply both sides of the second equation by 2:
\[
2 + y_2 = 10 \implies y_2 = 10 - 2 \implies y_2 = 8
\]

Therefore, the coordinates of point K are \( (13, 8) \).

The correct answer is:

A. (13, 8)