Apply geometric motions to reflect figures. Brinda reflects point T(2, 3)

Question

𝑇
(
2
,

3
)
over a line of reflection, resulting in point T′(2, −5)
𝑇
′
(
2
,

−
5
)
. What must be true?(1 point)
Responses

The line of reflection is x=−1
𝑥
=
−
1
.
The line of reflection is x is equal to negative 1 .

The line of reflection is the y-axis.
The line of reflection is the y -axis.

The line of reflection is the x-axis.
The line of reflection is the x -axis.

The line of reflection is y=−1
𝑦
=
−
1
.

Answer 1

To find the line of reflection for the points \( T(2, 3) \) and \( T'(2, -5) \), we need to determine the midpoint of these two points. The line of reflection will bisect the segment connecting \( T \) and \( T' \) perpendicularly.

1. Calculate the midpoint of points \( T(2, 3) \) and \( T'(2, -5) \):

   \[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{2 + 2}{2}, \frac{3 + (-5)}{2} \right) = \left( 2, \frac{-2}{2} \right) = (2, -1) \]

2. Determine the line of reflection: Since \( T \) and \( T' \) have the same x-coordinate (2) and different y-coordinates, the line of reflection must be horizontal. The midpoint's y-coordinate is -1, which suggests that the line of reflection is \( y = -1 \).

Thus, the correct statement is:

The line of reflection is \( y = -1 \).