Question

What are the coordinates of point Q
after it is reflected across the line x=−2
?

(1 point)
Q(−4,3)→Q′
(
,
)

Answer 1

To reflect a point across the line \( x = -2 \), you need to determine how far the point is from the line and then place the reflected point the same distance on the opposite side of the line.

1. The original point \( Q \) is at \( (-4, 3) \).
2. The line \( x = -2 \) is vertical.
3. The distance from \( Q(-4, 3) \) to the line \( x = -2 \) is calculated as follows:

- The x-coordinate of \( Q \) is \( -4 \).
- The x-coordinate of the line \( x = -2 \) is \( -2 \).
- The distance from \( -4 \) to \( -2 \) is:

\[
-4 - (-2) = -4 + 2 = -2
\]

4. So, \( Q(-4, 3) \) is 2 units to the left of the line \( x = -2 \).

5. To find the reflected point \( Q' \), move 2 units to the right of the line \( x = -2 \):

- The x-coordinate of \( Q' \) will be:

\[
-2 + 2 = 0
\]

6. The y-coordinate remains the same, so it stays at \( 3 \).

Therefore, the coordinates of the reflected point \( Q' \) are \( (0, 3) \).

Thus, \( Q(-4, 3) \) reflects to \( Q'(0, 3) \).