Question

The vertices of a triangle are A(1,1), B(1,4), C(3,1). Reflect the triangle over the x-axis. Graph both triangles.

a) Triangle ABC: A(1,1), B(1,4), C(3,1), A'(1,-1), B'(1,-4), C'(3,-1)
b) Triangle ABC: A(1,1), B(1,4), C(3,1), A'(1,-1), B'(1,-4), C'(3,-1)
c) Triangle ABC: A(1,1), B(1,4), C(3,1), A'(1,1), B'(1,4), C'(3,1)
d) Triangle ABC: A(1,1), B(1,4), C(3,1), A'(1,3), B'(1,4), C'(3,3)

Answer 1

To reflect the triangle over the x-axis, change the signs of the y-coordinates of the vertices. Graph both triangles to compare their positions.

Step-by-step explanation:

To reflect the triangle over the x-axis, we need to change the signs of the y-coordinates of the vertices.

For example, the reflection of point A(1,1) will be A'(1,-1) because the x-coordinate remains the same, but the y-coordinate changes to its opposite. Similarly, point B(1,4) will be reflected to B'(1,-4) and point C(3,1) will be reflected to C'(3,-1).

After reflecting the points, we can graph both triangles to compare their positions. Triangle ABC will be on the upper side of the x-axis, while the reflected triangle A'B'C' will be on the lower side of the x-axis.