Question

1. draw what the new image looks like after the rule: translation: 2 units right and 3 units up reflection across the y - axis

Explanation:

Step1: Translation

For a point \((x,y)\), a translation of \(2\) units right and \(3\) units up changes the coordinates to \((x + 2,y+3)\).

Step2: Reflection across the \(y\) - axis

The rule for reflection across the \(y\) - axis is \((x,y)\to(-x,y)\). So, if after translation a point has coordinates \((x',y')=(x + 2,y + 3)\), after reflection the coordinates become \((- (x + 2),y+3)\)

Answer:

1. First, take each vertex of the original triangle (for example, if a vertex of \(\triangle ZXY\) has coordinates \((x,y)\)):

• Apply the translation: new coordinates \((x + 2,y+3)\)
• Then apply the reflection across the \(y\) - axis: new coordinates \((-(x + 2),y + 3)\)

1. Repeat this process for all vertices of the original figure.
2. Connect the new vertices to form the final image.