Question

triangle abc has coordinates listed below.
points x y
a -5 3
b -8 1
c -3 4
if the triangle is reflected over the line x = 0 and then translated 8 units down, what are the coordinates of point b?
(-8, -1)
(8, -7)
(-8, -9)
(8, 1)

Explanation:

Step1: Reflect point B over x = 0

The rule for reflecting a point $(x,y)$ over the line $x = 0$ (y - axis) is $(-x,y)$. Point B has coordinates $(-8,1)$. After reflection over the y - axis, the x - coordinate changes sign. So the new coordinates are $(8,1)$.

Step2: Translate the reflected point 8 units down

The rule for translating a point $(x,y)$ down by $k$ units is $(x,y - k)$. Here $k = 8$. So for the point $(8,1)$, the new y - coordinate is $1-8=-7$. The final coordinates of point B are $(8,-7)$.

Answer:

B. $(8, -7)$