Question

graph the image of parallelogram j k l m after a reflection over the line y = 5.

Explanation:

Step1: Find the distance between each point and the line \(y = 5\)

For a point \((x,y)\), the distance \(d\) from the line \(y = 5\) is \(d=\vert y - 5\vert\).
For point \(J(-9,8)\): \(d=\vert8 - 5\vert=3\).
For point \(K(-1,8)\): \(d=\vert8 - 5\vert=3\).
For point \(L(3,9)\): \(d=\vert9 - 5\vert=4\).
For point \(M(-4,9)\): \(d=\vert9 - 5\vert=4\).

Step2: Reflect each point over the line \(y = 5\)

The formula for reflecting a point \((x,y)\) over the line \(y = c\) is \((x,2c - y)\). Here \(c = 5\), so the formula is \((x,10 - y)\).
For \(J(-9,8)\): \(J'(-9,10 - 8)=(-9,2)\).
For \(K(-1,8)\): \(K'(-1,10 - 8)=(-1,2)\).
For \(L(3,9)\): \(L'(3,10 - 9)=(3,1)\).
For \(M(-4,9)\): \(M'(-4,10 - 9)=(-4,1)\).

Step3: Connect the reflected points

Connect \(J'(-9,2)\), \(K'(-1,2)\), \(L'(3,1)\) and \(M'(-4,1)\) to form the reflected parallelogram.

Answer:

Plot the points \(J'(-9,2)\), \(K'(-1,2)\), \(L'(3,1)\) and \(M'(-4,1)\) on the coordinate - plane and connect them to get the image of parallelogram \(JKLM\) after reflection over the line \(y = 5\).