Question

complete the equations identifying both lines of reflection that will flip the given figure onto itself. (1 point) x = 1 and y = 2 x = 3 and y = 1 x=-1 and y = 0 x = 6 and y=-1

Explanation:

Step1: Find the mid - point of the horizontal side

For the horizontal side with endpoints $A(-4,5)$ and $B(6,5)$, the formula for the mid - point of two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $x_1=-4,x_2 = 6,y_1 = 5,y_2 = 5$. So the mid - point is $(\frac{-4 + 6}{2},\frac{5+5}{2})=(1,5)$. For the horizontal side with endpoints $C(6,-1)$ and $D(-4,-1)$, the mid - point is $(\frac{-4 + 6}{2},\frac{-1-1}{2})=(1,-1)$. The vertical line of reflection for the rectangle is $x = 1$ (the line passing through the mid - points of the horizontal sides).

Step2: Find the mid - point of the vertical side

For the vertical side with endpoints $A(-4,5)$ and $D(-4,-1)$, the mid - point is $(\frac{-4-4}{2},\frac{5 - 1}{2})=(-4,2)$. For the vertical side with endpoints $B(6,5)$ and $C(6,-1)$, the mid - point is $(\frac{6 + 6}{2},\frac{5-1}{2})=(6,2)$. The horizontal line of reflection for the rectangle is $y = 2$ (the line passing through the mid - points of the vertical sides).

Answer:

$x = 1$ and $y=2$