Question

in the figure below, if you reflected △xyz over the y - axis, rotated 90° clockwise, and translated right 1 and down 2, what would be the coordinate of y?

Explanation:

Step1: Find Original Coordinate of Y

From the graph, the original coordinates of \( Y \) are \( (-3, 3) \) (since it's 3 units left on x - axis and 3 units up on y - axis).

Step2: Reflect over y - axis

The rule for reflection over the \( y \) - axis is \( (x,y)\to(-x,y) \).
Applying this to \( Y(-3,3) \), we get \( (3,3) \).

Step3: Rotate \( 90^{\circ} \) clockwise

The rule for a \( 90^{\circ} \) clockwise rotation is \( (x,y)\to(y, - x) \).
Applying this to \( (3,3) \), we substitute \( x = 3 \) and \( y = 3 \). So the new coordinates are \( (3,-3) \).

Step4: Translate right 1 and down 2

The rule for translation right \( a \) units and down \( b \) units is \( (x,y)\to(x + a,y - b) \). Here, \( a = 1 \) and \( b = 2 \).
Applying this to \( (3,-3) \), we have \( x=3 + 1=4 \) and \( y=-3-2=-5 \).

Answer:

The coordinate of the transformed \( Y \) is \( (4,-5) \)