Question

parallelogram abcd is reflected over the x - axis to map onto efgh. the coordinates of abcd are a(-5, 6), b(-7, 2), c(-1, 0), d(1, 4). what are the coordinates of efgh after the reflection?
e(-6, 5) f(-2, 7) g(0, 1) h(4, 1)
e(-5,-6) f(-7,-2) g(-1, 0) h(1,-4)
e(5,6) f(7, 2) g(1, 0) h(-1, 4)
e(6,-5) f(2,-7) g(0,-1) h(4, 1)

Explanation:

Step1: Recall reflection rule

When a point $(x,y)$ is reflected over the x - axis, the rule is $(x,y)\to(x, - y)$.

Step2: Apply rule to point A

For point $A(-5,6)$, after reflection over the x - axis, it becomes $E(-5,-6)$ since $x=-5$ and $y = 6$ changes to $-6$.

Step3: Apply rule to point B

For point $B(-7,2)$, after reflection over the x - axis, it becomes $F(-7,-2)$ as $x=-7$ and $y = 2$ changes to $-2$.

Step4: Apply rule to point C

For point $C(-1,0)$, after reflection over the x - axis, it remains $G(-1,0)$ because $y = 0$ and $0$ times $- 1$ is still $0$.

Step5: Apply rule to point D

For point $D(1,4)$, after reflection over the x - axis, it becomes $H(1,-4)$ as $x = 1$ and $y = 4$ changes to $-4$.

Answer:

B. E(-5,-6) F(-7,-2) G(-1,0) H(1,-4)