Question

complete the equations identifying both lines of reflection that will flip the given figure onto itself. (2 points) the lines of reflection are x = 1 and y = 1

Explanation:

Step1: Find vertical line of symmetry

The figure is symmetric about a vertical line. The mid - point between the left - most and right - most x - coordinates of the rectangle gives the vertical line of symmetry. The left - most x - coordinate is $x=-3$ and the right - most is $x = 5$. The mid - point is $\frac{-3 + 5}{2}=1$, so the vertical line of reflection is $x = 1$.

Step2: Find horizontal line of symmetry

The figure is symmetric about a horizontal line. The mid - point between the top - most and bottom - most y - coordinates of the rectangle gives the horizontal line of symmetry. The top - most y - coordinate is $y = 4$ and the bottom - most is $y=-2$. The mid - point is $\frac{4+( - 2)}{2}=1$, so the horizontal line of reflection is $y = 1$.

Answer:

The lines of reflection are $x = 1$ and $y = 1$