Question

1. graph triangle jkl after a translation left 1 unit and down 5 units.

Explanation:

Step1: Find the original coordinates

From the graph, we can see that the coordinates of point \(L\) are \((1,1)\), the coordinates of point \(J\) are \((4,5)\), and the coordinates of point \(K\) are \((5,1)\).

Step2: Apply the translation rule

The translation rule for moving left \(1\) unit and down \(5\) units is \((x,y)\to(x - 1,y-5)\).
For point \(L(1,1)\):
\(x=1,y = 1\)
\(x-1=1 - 1=0\)
\(y - 5=1-5=-4\)
The new coordinates of \(L'\) are \((0,-4)\)
For point \(J(4,5)\):
\(x = 4,y=5\)
\(x-1=4-1 = 3\)
\(y-5=5 - 5=0\)
The new coordinates of \(J'\) are \((3,0)\)
For point \(K(5,1)\):
\(x=5,y = 1\)
\(x-1=5-1=4\)
\(y-5=1-5=-4\)
The new coordinates of \(K'\) are \((4,-4)\)

Step3: Graph the new triangle

Plot the points \(L'(0,-4)\), \(J'(3,0)\) and \(K'(4,-4)\) on the coordinate - plane and connect them to form triangle \(J'K'L'\)

Answer:

The new coordinates of the vertices of the translated triangle are \(L'(0,-4)\), \(J'(3,0)\) and \(K'(4,-4)\). Graph these points and connect them to get the translated triangle.