Question

graph the image of trapezoid jklm after a reflection over the line x = -1.

Explanation:

Step1: Find coordinates of vertices

First, identify the coordinates of trapezoid \(JKLM\):

• \(J(-9, 2)\)
• \(K(-6, 2)\)
• \(L(-3, 4)\)
• \(M(-10, 4)\)

Step2: Reflect over \(x = -1\)

The formula for reflecting a point \((x, y)\) over the vertical line \(x = a\) is \((2a - x, y)\). Here, \(a=-1\), so the reflection formula is \((2(-1)-x, y)=(-2 - x, y)\).

• For \(J(-9, 2)\):

New \(x\)-coordinate: \(-2-(-9)=7\), so \(J'=(7, 2)\)

• For \(K(-6, 2)\):

New \(x\)-coordinate: \(-2-(-6)=4\), so \(K'=(4, 2)\)

• For \(L(-3, 4)\):

New \(x\)-coordinate: \(-2-(-3)=1\), so \(L'=(1, 4)\)

• For \(M(-10, 4)\):

New \(x\)-coordinate: \(-2-(-10)=8\), so \(M'=(8, 4)\)

Step3: Plot the reflected points

Plot \(J'(7, 2)\), \(K'(4, 2)\), \(L'(1, 4)\), and \(M'(8, 4)\) on the grid and connect them to form the reflected trapezoid.

Answer:

The reflected trapezoid has vertices at \(J'(7, 2)\), \(K'(4, 2)\), \(L'(1, 4)\), and \(M'(8, 4)\) (plotted on the grid as described).