Question

write the coordinates of the vertices after a translation 8 units left and 1 unit down.

Explanation:

Step1: Determine the original coordinates

From the graph, the original coordinates are \(J(2,0)\), \(K(2,1)\), \(L(8,1)\), \(M(8,0)\).

Step2: Apply the translation rule

The translation rule for 8 units left (subtract 8 from \(x\)-coordinate) and 1 unit down (subtract 1 from \(y\)-coordinate) is \((x,y)\to(x - 8,y-1)\).

• For \(J(2,0)\): \(x=2,y = 0\), \(x-8=2 - 8=-6\), \(y - 1=0-1=-1\), so \(J'(-6,-1)\).
• For \(K(2,1)\): \(x=2,y = 1\), \(x-8=2 - 8=-6\), \(y - 1=1-1=0\), so \(K'(-6,0)\).
• For \(L(8,1)\): \(x=8,y = 1\), \(x-8=8 - 8=0\), \(y - 1=1-1=0\), so \(L'(0,0)\).
• For \(M(8,0)\): \(x=8,y = 0\), \(x-8=8 - 8=0\), \(y - 1=0-1=-1\), so \(M'(0,-1)\).

Answer:

\(J'(-6,-1)\), \(K'(-6,0)\), \(L'(0,0)\), \(M'(0,-1)\)