Exercise 46 Page 634

Before we begin, let's review the three main types of reflections on a coordinate plane.

1. A reflection in the x -axis changes the sign of the y-variable: (x,y) → (x, - y).
2. A reflection in the y -axis changes the sign of the x-variable: (x,y) → (- x, y).
3. A reflection in the line y=x interchanges the x- and y-variables: (x,y) → (y,x).

Now, let's plot the given vertices and graph the figure.

Since we want to reflect the triangle ABC in the x -axis, we have to change the sign of the y-coordinates of each vertex.

(x,y)	(x,- y)
A(-2,4)	A'(-2,-4)
B(3,1)	B'(3,-1)
C(0,- 2)	C'(0,2)

Finally, we can plot the new vertices and graph the reflected image.

We found that the coordinates of the vertices are A'(-2,-4), B'(3,-1) and C'(0,2). Therefore, the correct answer is B.