Question

figure defgh is reflected across the y - axis to form figure defgh. determine whether each statement is true. select true or false for each statement. e is located two units above the x - axis. the y - coordinate of d is the opposite of the y - coordinate of d. the x - coordinate of h is the opposite of the x - coordinate of h. gh = gh m∠f = m∠f g is located at (2,4)

Explanation:

Step1: Recall reflection rule across y - axis

The rule for reflecting a point $(x,y)$ across the $y$-axis is $(-x,y)$.

Step2: Analyze statement about $E'$

From the graph, assume the $y$-coordinate of $E$ is $ - 2$. After reflection across the $y$-axis, the $y$-coordinate of $E'$ is still $-2$, which is 2 units below the $x$-axis. So the statement " $E'$ is located two units above the $x$-axis" is False.

Step3: Analyze statement about $D'$

When reflecting a point across the $y$-axis, the $y$-coordinate remains the same. So the statement "The $y$-coordinate of $D'$ is the opposite of the $y$-coordinate of $D$" is False.

Step4: Analyze statement about $H'$

By the rule of reflection across the $y$-axis $(x,y)\to(-x,y)$, the $x$-coordinate of $H'$ is the opposite of the $x$-coordinate of $H$. So this statement is True.

Step5: Analyze statement about $G'H'$ and $GH$

Reflection is a rigid - motion, which preserves distances. So $G'H'=GH$. This statement is True.

Step6: Analyze statement about $\angle F'$ and $\angle F$

Reflection preserves angles. So $m\angle F' = m\angle F$. This statement is True.

Step7: Analyze statement about $G'$

Assume the coordinates of $G$ are $(- 2,-4)$. After reflection across the $y$-axis, the coordinates of $G'$ are $(2,-4)$, not $(2,4)$. So this statement is False.

Answer:

False
False
True
True
True
False