Question

1. triangle xyz, shown in the diagram below, is reflected over the line ( x = 2 ). state the coordinates of ( \triangle xyz ), the image of ( \triangle xyz ).

Explanation:

Step1: Find the distance from each point to the line \(x = 2\)

For a point \((x,y)\) reflected over the line \(x=a\), the formula for the \(x -\) coordinate of the reflected point \((x',y')\) is \(x'=2a - x\), and \(y'=y\). Here \(a = 2\).
The coordinates of \(X\) are \((1,-1)\), \(Y\) are \((0,1)\), \(Z\) are \((-2,1)\)

Step2: Calculate the \(x -\) coordinate of the reflected points

For point \(X\):
Using the formula \(x'=2\times2-1\), we get \(x' = 3\), \(y'=-1\), so \(X'=(3,-1)\)
For point \(Y\):
Using the formula \(x'=2\times2 - 0\), we get \(x'=4\), \(y' = 1\), so \(Y'=(4,1)\)
For point \(Z\):
Using the formula \(x'=2\times2-(-2)\), we get \(x'=4 + 2=6\), \(y'=1\), so \(Z'=(6,1)\)

Answer:

The coordinates of \(X'\) are \((3, -1)\), \(Y'\) are \((4,1)\), \(Z'\) are \((6,1)\)