Question

complete the table to show the coordinates of figure efgh and its image.
figure efgh | figure efgh
e(-3, 4) | ?
f(-1, 4) | e(3, 4)
g(-2, 1) | e(-3, 4)
h(-4, 3) | e(4, 3)
| e(-4, 3)

Explanation:

Step1: Identify transformation rule

Compare $F(-1,4) \to E'(3,4)$: $-1 \to 3 = -(-1) + 2$; $y$-value stays 4.
Check $H(-4,3) \to E'(4,3)$: $-4 \to 4 = -(-4) + 0$? Correct rule: reflect over y-axis: $(x,y) \to (-x,y)$.
Verify: $F(-1,4) \to (1,4)$? Wait, typo in table: $F$ maps to $F'(1,4)$, but table mislabels as $E'$. Correct rule: $(x,y) \to (-x,y)$.

Step2: Apply rule to $E(-3,4)$

Substitute $x=-3, y=4$ into $(-x,y)$.
$\text{New } x = -(-3) = 3$, $y=4$.

Answer:

$E'(3,4)$

Note: The table has labeling errors (all image points are mislabeled $E'$ instead of $F', G', H'$). The correct image of $E(-3,4)$ under reflection over the y-axis is $(3,4)$.