Question

apply geometric motions to reflect figures. brinda reflects point t(2, 3) over a line of reflection, resulting in point t(2, - 5). what must be true? (1 point)
the line of reflection is the x - axis.
the line of reflection is x = - 1.
the line of reflection is the y - axis.
the line of reflection is y = - 1.

Explanation:

Step1: Recall reflection property

When a point $(x,y)$ is reflected over a horizontal line $y = k$, the $x$-coordinate remains the same and the distance between $y$ and $k$ is equal to the distance between the new - $y$ coordinate and $k$.

Step2: Calculate the mid - point of $y$ values

The original point is $T(2,3)$ and the reflected point is $T'(2, - 5)$. The $x$-coordinates are the same ($x = 2$ for both points). Let the line of reflection be $y=k$. The mid - point of the $y$ values of the point and its reflection gives the equation for $k$. Using the mid - point formula for $y$ values: $k=\frac{y + y'}{2}$, where $y = 3$ and $y'=-5$. So $k=\frac{3+( - 5)}{2}=\frac{3 - 5}{2}=\frac{-2}{2}=-1$.

Answer:

The line of reflection is $y = - 1$.