∆ABChas vertices A(–1, –2), B(–4, –4), and
C(–3, –5). Graph ∆ABC and its image after a
reflection over the x-axis. Name the
coordinates of the vertices of the reflected
triangle...is it A(1,-2), B(3, -4), C(2,-5) or A(-1,2), B(-3,4), C(-2,5)
such a reflection takes (x,y) -> (x,-y), so it is neither set of vertices. You want
(–1,2), (–4,4), (–3,5)
To graph the given triangle ∆ABC and its image after a reflection over the x-axis, we can follow these steps:
1. Plot the original triangle ∆ABC using the given coordinates for its vertices: A(–1, –2), B(–4, –4), and C(–3, –5).
- Plot point A at (-1, -2)
- Plot point B at (-4, -4)
- Plot point C at (-3, -5)
2. To reflect the triangle over the x-axis, we need to keep the x-coordinates the same but change the sign of the y-coordinates of each vertex.
So, the coordinates of the vertices of the reflected triangle will be:
- A' will have the same x-coordinate as A but the sign of the y-coordinate will be reversed. Therefore, A' will be (–1, 2).
- B' will have the same x-coordinate as B but the sign of the y-coordinate will be reversed. Therefore, B' will be (–4, 4).
- C' will have the same x-coordinate as C but the sign of the y-coordinate will be reversed. Therefore, C' will be (–3, 5).
Thus, the correct coordinates for the vertices of the reflected triangle are A(–1, 2), B(–4, 4), and C(–3, 5).