Question

1. translate the triangle 4 units right and 3 units down.

Explanation:

Step1: Identify original coordinates

The original coordinates of the vertices of the triangle are \(J(0,3)\), \(K(0,1)\), \(L(- 4,1)\).

Step2: Apply the translation rule

The translation rule for moving 4 units right and 3 units down is \((x,y)\to(x + 4,y-3)\).
For point \(J(0,3)\): \(x=0,y = 3\), after translation \(x'=0 + 4=4,y'=3-3 = 0\), so the new - coordinate of \(J\) is \((4,0)\).
For point \(K(0,1)\): \(x = 0,y=1\), after translation \(x'=0 + 4=4,y'=1-3=-2\), so the new - coordinate of \(K\) is \((4,-2)\).
For point \(L(-4,1)\): \(x=-4,y = 1\), after translation \(x'=-4 + 4=0,y'=1-3=-2\), so the new - coordinate of \(L\) is \((0,-2)\).

Answer:

\(J(4,0)\), \(K(4,-2)\), \(L(0,-2)\)