Question

transformations transformations unit test
image long description
complete the equations identifying both lines of reflection that will flip the given figure onto itself.
(1 point)
the lines of reflection are x = and y =

Explanation:

Step1: Find the line of reflection for x - axis

For a rectangle with vertices \(A(-4,5)\), \(B(6,5)\), \(C(6, - 1)\) and \(D(-4,-1)\), the mid - point of the segment joining \(A\) and \(B\) (and also \(C\) and \(D\)) in the x - direction gives the vertical line of reflection. The formula for the mid - point of two points \((x_1,y_1)\) and \((x_2,y_2)\) in the x - direction is \(x=\frac{x_1 + x_2}{2}\). Here \(x_1=-4\) and \(x_2 = 6\), so \(x=\frac{-4 + 6}{2}=1\).

Step2: Find the line of reflection for y - axis

The mid - point of the segment joining \(A\) and \(D\) (and also \(B\) and \(C\)) in the y - direction gives the horizontal line of reflection. The formula for the mid - point of two points \((x_1,y_1)\) and \((x_2,y_2)\) in the y - direction is \(y=\frac{y_1 + y_2}{2}\). Here \(y_1 = 5\) and \(y_2=-1\), so \(y=\frac{5+( - 1)}{2}=2\).

Answer:

The lines of reflection are \(x = 1\) and \(y=2\)