Question

use what youve learned so far to identify each transformation. give both a verbal description and an algebraic representation of each transformation below.
2.
verbal description
algebraic representation
verbal description: choose your answer... algebraic representation: (x, y)→(-x, -y)
choose your answer.
translation right 10
rotation 180 degrees
cw/ccw
reflection over x - axis
rotation 90 degrees
(ccw) 90 degrees (cw)
reflection over y - axis
x, y → (x, -y)
3
part 1 identifying transformations
transformation. give both a verbal description and an algebraic representation of each

Explanation:

Step1: Analyze the algebraic representation

The algebraic representation is \((x, y) \to (-x, -y)\). This is the rule for a 180 - degree rotation about the origin. In a 180 - degree rotation, both the x - coordinate and y - coordinate of a point are negated.

Step2: Match with the verbal description options

• "translation right 10": A translation would involve adding or subtracting a constant to the x or y coordinate, not negating them. So this is incorrect.
• "rotation 180 degrees (CW/CCW)": A 180 - degree rotation (clockwise or counter - clockwise) about the origin has the rule \((x,y)\to(-x, -y)\), which matches the given algebraic representation.
• "reflection over x - axis": The rule for reflection over the x - axis is \((x,y)\to(x, -y)\), which does not match \((x,y)\to(-x, -y)\).
• "rotation 90 degrees (CW/CCW)": The rule for a 90 - degree clockwise rotation is \((x,y)\to(y, -x)\) and for a 90 - degree counter - clockwise rotation is \((x,y)\to(-y,x)\), which do not match \((x,y)\to(-x, -y)\).
• "reflection over y - axis": The rule for reflection over the y - axis is \((x,y)\to(-x,y)\), which does not match \((x,y)\to(-x, -y)\).
• "reflection over \(y = x\)": The rule for reflection over \(y=x\) is \((x,y)\to(y,x)\), which does not match \((x,y)\to(-x, -y)\).

Answer:

Verbal Description: rotation 180 degrees (CW/CCW)
Algebraic Representation: \((x, y)\to(-x, -y)\)