Question

if the figure below has been reflected across the y-axis, what are the coordinates of the preimage? p blank q blank r blank

Explanation:

Step1: Recall reflection over y - axis rule

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

Step2: Find coordinates of $P'$, $Q'$, $R'$

From the graph:

• Coordinates of $P'$: Looking at the graph, $P'$ is at $(3,4)$.
• Coordinates of $Q'$: $Q'$ is at $(-2,1)$.
• Coordinates of $R'$: $R'$ is at $(1, - 5)$.

Step3: Apply reflection rule to find preimage coordinates

• For $P'=(3,4)$: Using the rule $(x,y)\to(-x,y)$, the preimage $P$ has coordinates $(-3,4)$ (since $x = 3$, so $-x=-3$ and $y = 4$ remains the same).
• For $Q'=(-2,1)$: Using the rule, the preimage $Q$ has coordinates $(2,1)$ (since $x=-2$, so $-x = 2$ and $y = 1$ remains the same).
• For $R'=(1,-5)$: Using the rule, the preimage $R$ has coordinates $(-1,-5)$ (since $x = 1$, so $-x=-1$ and $y=-5$ remains the same).

Answer:

$P(-3, 4)$, $Q(2, 1)$, $R(-1, -5)$