Question

translation right 10, up 2 (x,y)--> choose your answer... (x,-y) (y,-x) (-y,x) (-x,y) over the y - axis over the x - axis 270 counter - clockwise scale factor by 2 270 clockwise

Explanation:

To solve this, we analyze the transformation. First, identify a point from the original figure (e.g., \( P(-6, 4) \)) and its image \( P'(4, 6) \). Let's check the transformation rules:

Step 1: Recall rotation rules

• \( 270^\circ \) counter - clockwise rotation: \( (x,y)\to(-y,x) \)
• \( 270^\circ \) clockwise rotation: \( (x,y)\to(y, - x) \)
• Reflection over x - axis: \( (x,y)\to(x, - y) \)
• Reflection over y - axis: \( (x,y)\to(-x,y) \)

Let's take point \( P(-6,4) \). If we apply \( (y,-x) \) (which is \( 270^\circ \) clockwise rotation: \( (x,y)\to(y, - x) \)):
For \( x=-6,y = 4 \), \( y=4 \) and \( -x = 6 \), so the new point is \( (4,6) \), which matches \( P' \).

Let's verify with another point, say \( S(-3,2) \). Applying \( (y,-x) \): \( y = 2 \), \( -x=3 \), so the new point is \( (2,3) \), which matches \( S'(2,3) \).

Answer:

\((y, - x)\)