Question

△ efg has coordinates e(-3, -5), f(-9, 1), and g(-6, 4). what are the coordinates of the vertices of the image after a reflection in the x - axis?

a) e(3, -5), f(9, 1), and g(6, 4)
b) e(5, 3), f(1, 9), and g(-4, 6)
c) e(5, -3), f(-1, 9), and g(4, -6)
d) e(-3, 5), f(-9, -1), and g(-6, -4)

Explanation:

Step1: Recall reflection rule

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

Step2: Apply rule to point E

For point $E(-3,-5)$, after reflection over the $x - axis$, $x=-3$ and $y = -(-5)=5$. So $E'(-3,5)$.

Step3: Apply rule to point F

For point $F(-9,1)$, after reflection over the $x - axis$, $x=-9$ and $y=-1$. So $F'(-9,-1)$.

Step4: Apply rule to point G

For point $G(-6,4)$, after reflection over the $x - axis$, $x=-6$ and $y = - 4$. So $G'(-6,-4)$.

Answer:

D. $E'(-3,5),F'(-9,-1),G'(-6,-4)$