Question

rhombus jklm with vertices j(-4,7), k(0,8), l(-1,4), and m(-5,3): (x,y)→(x + 2,y - 2)
j (__,__)
k (__,__)
l (__,__)
m (__,__)

Explanation:

Step1: Find the new \(x\) - coordinate for each vertex

For a point \((x,y)\) with the transformation \((x,y)\to(x + 2,y-2)\), we add \(2\) to the \(x\) - coordinate.

• For \(J(-4,7)\): \(x=-4\), new \(x=-4 + 2=-2\)
• For \(K(0,8)\): \(x = 0\), new \(x=0 + 2=2\)
• For \(L(-1,4)\): \(x=-1\), new \(x=-1+2 = 1\)
• For \(M(-5,3)\): \(x=-5\), new \(x=-5 + 2=-3\)

Step2: Find the new \(y\) - coordinate for each vertex

We subtract \(2\) from the \(y\) - coordinate.

• For \(J(-4,7)\): \(y = 7\), new \(y=7-2 = 5\)
• For \(K(0,8)\): \(y = 8\), new \(y=8-2=6\)
• For \(L(-1,4)\): \(y = 4\), new \(y=4-2 = 2\)
• For \(M(-5,3)\): \(y = 3\), new \(y=3-2=1\)

Answer:

\(J'(-2,5)\)
\(K'(2,6)\)
\(L'(1,2)\)
\(M'(-3,1)\)