Suppose △ABC has coordinates A(2, 3), B(5, 1), C(4, 4), and △ABC is mapped to △A′B′C′ by a reflection across the line y = 5 followed by a translation 1 unit down. select all the statements that are true about the coordinates of △A′B′C′.
A. A'(2, 2), B'(5, 0), C'(4, 3)
B. A'(3, 2), B'(6, 0), C'(5, 3)
C. A'(1, 2), B'(4, 0), C'(3, 3)
D. A'(2, 4), B'(5, 2), C'(4, 5)
A. A'(2, 2), B'(5, 0), C'(4, 3)
C. A'(1, 2), B'(4, 0), C'(3, 3)
AAAaannndd the bot gets it wrong yet again!
well, x will not change, so that eliminates B and C.
In fact, I suspect a typo, since none of the choices is correct.
for example, (2,3)→(2,7)→(2,6)
a and b
To find the coordinates of △A'B'C' after the reflection and translation, you can follow these steps:
1. Reflection across the line y = 5: To reflect a point across a line, you can subtract the y-coordinate of the point from the equation of the line and double the result.
A': Reflect A(2, 3) across y = 5.
Subtract 3 from 5 and double the result: 5 - 3 = 2 * 2 = 4.
The x-coordinate remains the same: x = 2.
So, A' = (2, 4).
B': Reflect B(5, 1) across y = 5.
Subtract 1 from 5 and double the result: 5 - 1 = 2 * 4 = 8.
The x-coordinate remains the same: x = 5.
So, B' = (5, 8).
C': Reflect C(4, 4) across y = 5.
Subtract 4 from 5 and double the result: 5 - 4 = 2 * 1 = 2.
The x-coordinate remains the same: x = 4.
So, C' = (4, 2).
2. Translation 1 unit down: To translate a point, subtract 1 from the y-coordinate.
A'': Translate A' (2, 4) 1 unit down.
Subtract 1 from the y-coordinate: 4 - 1 = 3.
So, A'' = (2, 3).
B'': Translate B' (5, 8) 1 unit down.
Subtract 1 from the y-coordinate: 8 - 1 = 7.
So, B'' = (5, 7).
C'': Translate C' (4, 2) 1 unit down.
Subtract 1 from the y-coordinate: 2 - 1 = 1.
So, C'' = (4, 1).
Based on these calculations, we can conclude:
- A''(2, 3), B''(5, 7), and C''(4, 1) are the coordinates of △A'B'C' after the reflection across the line y = 5 followed by a translation 1 unit down.