Question

examine the image below. if $delta xyz$ is reflected across the y - axis then rotate 90°, what are the coordinates of $x$?
(-2, -3)
(-3, 2)
(3, 2)
(2, -1)

Explanation:

Step1: Find coordinates after reflection

The coordinates of point $X$ are $(-3, 2)$. When reflecting a point $(x,y)$ across the $y$-axis, the rule is $(-x,y)$. So for $X(-3,2)$, after reflection across the $y$-axis, the new coordinates $X'$ are $(3,2)$.

Step2: Find coordinates after rotation

The rule for rotating a point $(x,y)$ counter - clockwise by $90^{\circ}$ about the origin is $(-y,x)$. For the point $X'(3,2)$, after rotation, we have $x = 3$ and $y = 2$. Using the rotation rule, the new coordinates $X''$ are $(-2,3)$. But if it's a clock - wise rotation of $90^{\circ}$ (rule is $(y,-x)$), for $X'(3,2)$ we get $X''=(2,-3)$. Since the problem doesn't specify the direction of rotation and clock - wise is more common in some contexts, we assume clock - wise rotation here.

Answer:

$(2,-3)$