he vertices of triangle ABC are A(-2,5) ,B(-2,3), and C(-5,3). Triangle ABC is reflected across the x-axis to produce the image triangle A''B''C''. Graph triangle ABC and triangle A''B''C''.
Which graph shows triangle ABC and triangle A''B''C'' ?
reflection across the x-axis takes (x,y) → (x,-y)
so just flip the sign of all the y-values.
To graph triangle ABC, we plot the three given vertices A(-2, 5), B(-2, 3), and C(-5, 3) on a coordinate plane.
Now, to reflect triangle ABC across the x-axis to produce the image triangle A''B''C'', we need to keep the x-coordinates the same but change the sign of the y-coordinates. This means that point A(-2, 5) becomes A''(-2, -5), B(-2, 3) becomes B''(-2, -3), and C(-5, 3) becomes C''(-5, -3).
The graph that shows both triangle ABC and A''B''C'' is:
First, plot the points of triangle ABC:
A(-2, 5), B(-2, 3), C(-5, 3)
Then plot the points of triangle A''B''C'':
A''(-2, -5), B''(-2, -3), C''(-5, -3)
The graph will look like:
```
|
A'' | C''
______|_________
B'' _| C
|/
A'|
____|_________
B
```
To graph triangle ABC and triangle A''B''C'', we need to plot the given vertices on a coordinate plane and then reflect the points across the x-axis.
First, let's plot the vertices of triangle ABC:
A(-2, 5)
B(-2, 3)
C(-5, 3)
Now, let's reflect these points across the x-axis to obtain the corresponding vertices A''B''C'':
A''(-2, -5)
B''(-2, -3)
C''(-5, -3)
To draw the graphs, we can use a coordinate plane with the x and y axes labeled.
In triangle ABC:
- Connect the points A, B, and C with straight lines to form a triangle.
In triangle A''B''C'':
- Connect the points A'', B'', and C'' with straight lines to form another triangle.
Please note that I cannot provide visual images as I am a text-based AI bot. However, with the given coordinates and the instructions provided, you should be able to graph the triangles on a coordinate plane.