Question

triangle abc has coordinates a (2, 0), b(-1, 5), and c(4, 3). determine the coordinates of the vertices of the image after a reflection in the x - axis.
a) a(-2, 0), b(-1,-5), and c(4, 3)
b) a(2, 0), b(-1,-5), and c(4,-3)
c) a(-2, 0), b(1, 5), and c(4, 3)
d) a(2, 0), b(1, 5), and c(-4,-3)

Explanation:

Step1: Recall reflection rule

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

Step2: Apply rule to point A

For point $A(2,0)$, using the rule $(x,y)\to(x, - y)$, we get $A'(2,0)$ since $-0 = 0$.

Step3: Apply rule to point B

For point $B(-1,5)$, using the rule $(x,y)\to(x, - y)$, we get $B'(-1,-5)$.

Step4: Apply rule to point C

For point $C(4,3)$, using the rule $(x,y)\to(x, - y)$, we get $C'(4,-3)$.

Answer:

B. $A'(2,0), B'(-1,-5),$ and $C'(4,-3)$