Question

1. translation: 5 left and 2 up

Explanation:

Step1: Identify original vertices

First, find the coordinates of the original triangle's vertices. From the graph:

• Left vertex: \((1, -1)\)
• Right vertex: \((4, -1)\)
• Bottom vertex: \((3, -5)\)

Step2: Apply translation rules

A translation of 5 left (subtract 5 from \(x\)-coordinate) and 2 up (add 2 to \(y\)-coordinate) uses the rule \((x, y) \to (x - 5, y + 2)\).

For \((1, -1)\):

\(x\)-new: \(1 - 5 = -4\)
\(y\)-new: \(-1 + 2 = 1\)
New vertex: \((-4, 1)\)

For \((4, -1)\):

\(x\)-new: \(4 - 5 = -1\)
\(y\)-new: \(-1 + 2 = 1\)
New vertex: \((-1, 1)\)

For \((3, -5)\):

\(x\)-new: \(3 - 5 = -2\)
\(y\)-new: \(-5 + 2 = -3\)
New vertex: \((-2, -3)\)

Answer:

The translated vertices are \((-4, 1)\), \((-1, 1)\), and \((-2, -3)\). To graph, plot these points and connect them.