Question

1. if a triangle with vertices at (2,2), (4,2), and (3,4) is reflected over the x - axis, what are the new coordinates of the vertex (3,4)?

a. (-3,4)
b. (3,-4)
c. (-3,-4)
d. (3,4)

Explanation:

Step1: Recall reflection rule over x - axis

When a point $(x,y)$ is reflected over the x - axis, the x - coordinate remains the same and the y - coordinate changes its sign. The rule is $(x,y)\to(x, - y)$.

Step2: Apply the rule to the given point

For the point $(3,4)$, using the rule $(x,y)\to(x, - y)$, we substitute $x = 3$ and $y = 4$. So, $(3,4)\to(3,-4)$.

Answer:

b. $(3,-4)$