Question

exit ticket seal the deal!

1. which rigid motion is shown in the diagram?
2. a translation moves ( b(-6,2) ) to ( b(3,1) ). what is the image of ( (x, y) ) under this translation?
3. what are the coordinates of ( (-3,7) ) after a counterclockwise rotation of ( 90^{circ} ) about the origin?
4. what is the image of ( a(-4,9) ) when it is reflected in the ( y )-axis?

Explanation:

Step1: Analyze translation

For a translation from \(B(-6,2)\) to \(B'(3,1)\), the horizontal change \(\Delta x=3 - (-6)=9\), the vertical change \(\Delta y = 1-2=-1\). So the translation rule is \((x,y)\to(x + 9,y-1)\)

Step2: Apply rotation rule

The rule for a counter - clockwise rotation of \(90^{\circ}\) about the origin is \((x,y)\to(-y,x)\). For the point \((-3,7)\), substituting \(x=-3\) and \(y = 7\) gives \((-7,-3)\)

Step3: Apply reflection rule

The rule for reflection in the \(y\) - axis is \((x,y)\to(-x,y)\). For the point \(A(-4,9)\), substituting \(x=-4\) and \(y = 9\) gives \((4,9)\)

Answer:

1. (No diagram provided, can't answer).
2. \((x + 9,y-1)\)
3. \((-7,-3)\)
4. \((4,9)\)