Question

what is the result of reflecting the point (-5, 7) over the x - axis and then translating it 3 units left? (-2, 7) (-8, 7) (-8, -7) (-2, -7)

Explanation:

Step1: Reflect over x - axis

When reflecting a point $(x,y)$ over the x - axis, the rule is $(x,y)\to(x, - y)$. Given the point $(-5,7)$, after reflecting over the x - axis, it becomes $(-5,-7)$.

Step2: Translate 3 units left

The rule for translating a point $(x,y)$ left by $a$ units is $(x,y)\to(x - a,y)$. Here $a = 3$, so for the point $(-5,-7)$, we have $x=-5$ and $y = - 7$. After translation, $x=-5-3=-8$ and $y=-7$. The new point is $(-8,-7)$.

Answer:

$(-8,-7)$