Question

1. which rigid motion is shown in the diagram?
2. a translation moves ( b(-6,2) ) to ( b^{prime}(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: Determine the rule for reflection over the y - axis

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\).

Step2: Apply the rule to the point \(A(-4,9)\)

For the point \(A(-4,9)\), when we apply the reflection rule \(x=-4\) becomes \(-x = 4\) and \(y = 9\) remains the same.

Answer:

The image of \(A(-4,9)\) when reflected in the \(y\) - axis is \((4,9)\)