Question

triangle xyz is reflected over a horizontal line of reflection to create triangle xyz. what are the coordinates of vertex x? (1 point) (-3, - 6) (-2, - 2) (-3, 8)

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ over a horizontal line, the $x -$coordinate remains the same, and the $y -$coordinate changes its distance from the line of reflection. If we assume the line of reflection is the $x -$axis (a common horizontal line of reflection), the rule for reflecting a point $(x,y)$ over the $x -$axis is $(x,-y)$.
The point $X$ has coordinates $(-3,8)$.

Step2: Apply the rule

For point $X(-3,8)$, using the rule $(x,-y)$, we get $X'(-3, - 8)$. But if we assume the line of reflection is $y = 2$ (for example, if we consider the mid - point between the original $y$ - value and the new $y$ - value based on the symmetry). The distance from $y = 8$ to $y = 2$ is $d=8 - 2=6$. So the new $y$ - value is $2-6=-4$. However, if we assume reflection over the $x -$axis:
The $x$ - coordinate of $X$ is $x=-3$ and the $y$ - coordinate of the reflected point $X'$ is $y=-8$. If we assume the line of reflection is $y = 1$ (and calculate the distance from $y = 8$ to $y = 1$ which is $7$), the new $y$ - value is $1 - 7=-6$.
Assuming reflection over the $x$ - axis (a common default for horizontal reflection if no other line is specified), for point $X(-3,8)$, the reflected point $X'$ has coordinates $(-3,-8)$. But if we assume the line of reflection is $y = 1$:
The distance from $y = 8$ to $y = 1$ is $7$. The new $y$ - value is $1-7=-6$ and $x$ remains $-3$. So the coordinates of $X'$ are $(-3,-6)$.

Answer:

$(-3,-6)$