Question

identifying and interpreting transform...

the result of reflecting a shape over the line ( y = x ) is that each point’s coordinates are ______________.

rotating a shape 270 degrees clockwise about the origin is equivalent to rotating it ______________ degrees counterclockwise.

Explanation:

First Question (Reflection over \( y = x \)):

Step1: Recall reflection over \( y = x \)

When a point \((x, y)\) is reflected over the line \( y = x \), the \( x \)-coordinate and \( y \)-coordinate swap places. So the coordinates of each point become \((y, x)\) (or we say the \( x \) and \( y \) coordinates are swapped).

Second Question (Rotation Equivalence):

Step1: Recall full rotation

A full rotation (clockwise or counterclockwise) is \( 360^\circ \).

Step2: Relate clockwise and counterclockwise

If we rotate \( 270^\circ \) clockwise, to find the equivalent counterclockwise rotation, we calculate \( 360^\circ - 270^\circ = 90^\circ \). So rotating \( 270^\circ \) clockwise is equivalent to rotating \( 90^\circ \) counterclockwise.

Answer:

s:

1. For the first blank: swapped (or "the \( x \) and \( y \) coordinates are interchanged" or more precisely "replaced by \( (y, x) \) where the original point is \( (x, y) \)")
2. For the second blank: \( 90 \)