Question

On a coordinate plane, triangle A B C has points (negative 3, negative 1), (negative 2, negative 3), (2, negative 1).
Triangle ABC is reflected over the line y = 1. What are the coordinates of B’?


(–2, 3)
(–2, 5)
(2, –3)
(4, –3)

Answer 1

To reflect a point over the line \(y = 1\), you can follow these steps:

1. Calculate the vertical distance from the point to the line \(y = 1\).
2. From the line \(y = 1\), move that same distance on the opposite side to find the reflected point.

Let's apply this to point \(B\) with coordinates \((-2, -3)\).

1. Calculate the distance from point \(B\) to the line \(y = 1\):
\[
\text{Distance} = y_B - 1 = -3 - 1 = -4
\]
The distance is -4, which means point \(B\) is 4 units below the line \(y = 1\).

2. Now, reflect this point by moving 4 units above the line:
\[
y' = 1 + 4 = 5
\]
The x-coordinate remains the same, so the reflected point \(B'\) will be:
\[
B' = (-2, 5)
\]

Thus, the coordinates of \(B'\) after reflecting point \(B\) over the line \(y = 1\) are \((-2, 5)\). The answer is:

**(–2, 5)**