Question

if $\triangle stu$ is reflected over the $y$-axis, what are the coordinates of the vertices of $\triangle stu$?
options:
$s(-3,-2), t(-2,-4), u(-1,-1)$
$s(3,2), t(2,4), u(1,1)$
$s(-3,2), t(-2,4), u(-1,1)$
$s(3,-2), t(2,-4), u(1,-1)$

Explanation:

Step1: Identify original coordinates

From the graph, we can determine the original coordinates of the vertices of $\triangle STU$. Let's assume the original coordinates:

• For point $S$: Looking at the graph, $S$ is at $(-3, 2)$ (since it's 3 units left of the y - axis and 2 units up).
• For point $T$: $T$ is at $(-2, 4)$ (2 units left of the y - axis and 4 units up).
• For point $U$: $U$ is at $(-1, 1)$ (1 unit left of the y - axis and 1 unit up).

Step2: Apply reflection over y - axis rule

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

• For point $S(-3,2)$:

Applying the rule, $x=-3$, so $-x = 3$. The reflected point $S'$ is $(3,2)$.

• For point $T(-2,4)$:

Applying the rule, $x = - 2$, so $-x=2$. The reflected point $T'$ is $(2,4)$.

• For point $U(-1,1)$:

Applying the rule, $x=-1$, so $-x = 1$. The reflected point $U'$ is $(1,1)$.

Answer:

$S'(3,2)$, $T'(2,4)$, $U'(1,1)$ (which corresponds to the option with $S(3,2)$, $T(2,4)$, $U(1,1)$)