Question

Triangle DEF has coordinates D(4,−1), E(5, 2), and F(1, 2). Determine the coordinates of the vertices of the image after a reflection in the x-axis.

A) D'(−4,−1), E'(−5, 2), and F'(−1, 2)

B) D'(4, 1), E'(5,−2), and F'(1,-2)

C) D'(5,−1), E'(6, 2), and F'(2, 2)

D) D'(1, 0), E'(2, 3), and F'(−2, 3)

Answer 1

B) D'(4, 1), E'(5,−2), and F'(1,-2)

Explanation:

When a point is reflected across the x-axis, the new x-coordinate remains unchanged but the new y-coordinate is the negative of the original y-coordinate

So the reflection results in the following new points

D(4, -1) ⇒ D'(4, 1)

E(5, 2) ⇒ E'(5, -2)

F(1, 2) ⇒ F'(1, -2)

So the correct answer choice is
B) D'(4, 1), E'(5,−2), and F'(1,-2)

Answer 2

B

Explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y )

that is the x- coordinate remains unchanged , while the y- coordinate is negated.

D (4, - 1 ) → D' (4, - (- 1) ) → D' (4, 1 )

E 5, 2 ) → E' (5, - 2 )

F (1, 2 ) → F' (1, - 2 )