Question

the points given below are the vertices of △vwx and its image after a reflection. v(2, 1), w(3, 5), x(4, 2) v( - 2, 1), w( - 3, 5), x( - 4, 2) a. what do you notice when you compare corresponding x - coordinates and corresponding y - coordinates of the vertices of △vwx and △vwx? b. what is the line of reflection?

Explanation:

Step1: Analyze x - coordinates

For point $V(2,1)$ and $V'(-2,1)$, $W(3,5)$ and $W'(-3,5)$, $X(4,2)$ and $X'(-4,2)$, the x - coordinates of the image points are the opposite of the x - coordinates of the original points. The y - coordinates remain the same.

Step2: Determine line of reflection

In a coordinate - plane, when the x - coordinates change sign and the y - coordinates remain the same, the line of reflection is the y - axis. The equation of the y - axis is $x = 0$.

Answer:

a. The x - coordinates of the vertices of $\triangle V'W'X'$ are the opposites of the x - coordinates of the vertices of $\triangle VWX$, while the y - coordinates remain the same.
b. The line of reflection is the y - axis or the line $x = 0$.