Question

a triangle is shown in the coordinate plane. graph the location of this triangle after a reflection across the line ( x = 1 ).

Explanation:

Step1: Find the original points

Assume the original triangle has vertices \(A(2,5)\), \(B(2,2)\), \(C(5,2)\)

Step2: Use the reflection formula

The formula for reflecting a point \((x,y)\) across the line \(x = a\) is \((2a - x,y)\). Here \(a = 1\), so the formula becomes \((2\times1 - x,y)=(2 - x,y)\)

For point \(A(2,5)\):
\(x = 2,y = 5\)
\(2 - x=2 - 2 = 0\)
The reflected point \(A'(0,5)\)

For point \(B(2,2)\):
\(x = 2,y = 2\)
\(2 - x=2 - 2 = 0\)
The reflected point \(B'(0,2)\)

For point \(C(5,2)\):
\(x = 5,y = 2\)
\(2 - x=2 - 5=-3\)
The reflected point \(C'(-3,2)\)

Step3: Plot the new points

Plot the points \(A'(0,5)\), \(B'(0,2)\) and \(C'(-3,2)\) and connect them to form the reflected triangle

Answer:

Plot the points \((0,5)\), \((0,2)\) and \((-3,2)\) and connect them.