Question

after a reflection of the figure, the image vertices are a(5, 1), b(3, -1), and c(7, -1). what is the line of reflection? o a. y = 2 o b. x = 2 o c. y = -x o d. y = 2x

Explanation:

Step1: Find mid - points of corresponding points

For a reflection, the line of reflection is the perpendicular bisector of the line segment joining a point and its image. Let's consider point \(A\) and \(A'\). First, we need to find the mid - point of the line segment \(AA'\). The mid - point formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Assume the coordinates of \(A\) can be found from the graph (let's say \(A(- 1,1)\)), for \(A(-1,1)\) and \(A'(5,1)\), the mid - point \(M_1\) of \(AA'\) is \((\frac{-1 + 5}{2},\frac{1+1}{2})=(2,1)\). For \(B\) (assume \(B(1,-1)\)) and \(B'(3,-1)\), the mid - point \(M_2\) of \(BB'\) is \((\frac{1 + 3}{2},\frac{-1-1}{2})=(2,-1)\). For \(C\) (assume \(C(-3,-1)\)) and \(C'(7,-1)\), the mid - point \(M_3\) of \(CC'\) is \((\frac{-3 + 7}{2},\frac{-1-1}{2})=(2,-1)\).

Step2: Determine the line of reflection

The mid - points of the line segments joining the pre - image and image points all lie on the line of reflection. Since the \(x\) - coordinate of the mid - points \((2,1)\), \((2,-1)\) is always \(2\), the equation of the line of reflection is \(x = 2\).

Answer:

B. \(x = 2\)