Question

triangle pqr has coordinates p(-1, 5), q(1, 2), and r(-3, -1). determine the coordinates of the vertices of the image after a reflection in the x - axis.
a) p(-1, -5), q(1, -2), and r(-3, 1)
b) p(-1, 5), q(1, 2), and r(-3, -1)
c) p(1, 5), q(-1, 2), and r(3, -1)
d) p(-1, -3), q(-1, -2), and r(-3, -1)

Explanation:

Step1: Recall reflection rule

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

Step2: Apply rule to point P

For point $P(-1,5)$, after reflection in the $x - axis$, the $x - coordinate$ remains the same and the $y - coordinate$ changes sign. So $P(-1,5)\to P'(-1,-5)$.

Step3: Apply rule to point Q

For point $Q(1,2)$, after reflection in the $x - axis$, we have $Q(1,2)\to Q'(1,-2)$.

Step4: Apply rule to point R

For point $R(-3,-1)$, after reflection in the $x - axis$, we get $R(-3,-1)\to R'(-3,1)$.

Answer:

The new coordinates of $P,Q,R$ are $P'(-1,-5),Q'(1,-2),R'(-3,1)$ which corresponds to option A.