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Question

A vertical line separates 2 triangles. The triangle to the left of the line is made up of points upper A (0,9), upper B(-5,5), and upper C (-5,-1), while the triangle on the right is made up of points upper A prime, upper B prime(11,5), and upper C prime.

Triangle ABC
has been reflected over a vertical line of reflection. The coordinates of vertices A
, B
, C
, and B′
are shown. What are the coordinates of vertex A′
?

(1 point)
The coordinates of vertex A′
are (
,
).
Remaining Attempts : 3
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Answer 1

To find the coordinates of vertex \( A' \) after reflecting \( A(0, 9) \) over a vertical line, we need to know the equation of the vertical line.

Since \( B(-5, 5) \) is reflected to \( B'(11, 5) \), we can find the vertical line of reflection. The midpoint of \( B \) and \( B' \) can help us find the line of reflection.

1. Calculate the midpoint: \[ \text{Midpoint of } B \text{ and } B' = \left( \frac{-5 + 11}{2}, \frac{5 + 5}{2} \right) = \left( \frac{6}{2}, 5 \right) = (3, 5) \]

This midpoint lies on the line of reflection, and since it’s a vertical line, the x-coordinate of the line of reflection is \( x = 3 \).

2. Now, to reflect point \( A(0, 9) \) across the line \( x = 3 \):
   • The horizontal distance from \( A \) to the line \( x = 3 \) is \( 3 - 0 = 3 \).
   • To reflect it, we move the same distance to the right of the line: \[ \text{New x-coordinate} = 3 + 3 = 6 \]
   • The y-coordinate remains the same, so it will still be \( 9 \).

Thus, the coordinates of vertex \( A' \) are \( (6, 9) \).

Final answer: The coordinates of vertex \( A' \) are \( (6, 9) \).