Question

#4. which best represent the transformation algebraically?
pre - image: q(-9, -8), r(-9, -2), s(-4, -2), t(-4, -8)
image: q(9, -8), r(9, -2), s(4, -2), t?
options:
○ (x, -y)
● (-x, y)
○ (-x, -y)
○ (x + 18, y)

Explanation:

Step1: Compare pre-image and image x-values

For $Q(-9,-8) \to Q'(9,-8)$: $-9 \to 9 = -(-9)$; For $R(-9,-2) \to R'(9,-2)$: $-9 \to 9 = -(-9)$; For $S(-4,-2) \to S'(4,-2)$: $-4 \to 4 = -(-4)$

Step2: Compare pre-image and image y-values

For all points, the y-value stays the same: $-8 \to -8$, $-2 \to -2$, $-2 \to -2$

Step3: Identify transformation rule

The x-coordinate is negated, y-coordinate unchanged: $(x,y) \to (-x,y)$

Step4: Find T' using the rule

For $T(-4,-8)$, apply $(-x,y)$: $-(-4)=4$, y remains $-8$, so $T'(4,-8)$

Answer:

The transformation rule is $\boldsymbol{(-x,y)}$, and the missing image point is $\boldsymbol{T'(4,-8)}$
Correct option: $\boldsymbol{(-x,y)}$