Question: Triangle Transformations
Original 1 Translate $ (x+2, y-1) $ 1 Reflect over y-axis 1 Rotate 90CCW about origin
Coordinate Summary:
Original:
A(1,2) B(4,2) C(2,5)
1. Translate $(x+2, y-1)$:
A'(3,1) B'(6,1) C'(4,4)
2. Reflect over y-axis:
A''(-3,1) B''(-6,1) C''(-4,4)
3. Rotate 90CCW about origin:
A'''(-1,-3) B'''(-1,-6) C'''(-4,-4)
Original triangle at top-right with vertices A(1,2), B(4,2), C(2,5).
Translated triangle at right with vertices A'(3,1), B'(6,1), C'(4,4).
Reflected triangle at left with vertices A''(-3,1), B''(-6,1), C''(-4,4).
Rotated final triangle at bottom-left with vertices A'''(-1,-3), B'''(-1,-6), C'''(-4,-4).
position_hint = top-rightMathematics 10
Seatwork Activity
Direction: In a graphing paper, draw a triangle with the vertices given below:
A(1,2)
B(4,2)
C(2,5)
Perform and draw the following transformations in order:
1. Translate the figure using $(x+2, y-1)$
2. Reflect the image across the y-axis
3. Rotate the final image 90 counterclockwise about the origin.
Graph/shape: triangle with vertices A(1,2), B(4,2), C(2,5), position_hint 1 {top-left, top-right, center, bottom-left, bottom-right}: top-left
User: Is this correct?
1. **State the problem:**
We are given a triangle with vertices $A(1,2)$, $B(4,2)$, and $C(2,5)$.
We need to perform three transformations in order:
- Translate by $(x+2, y-1)$
- Reflect over the y-axis
- Rotate 90 counterclockwise (CCW) about the origin
2. **Translate the triangle:**
Translation rule: $(x,y) \to (x+2, y-1)$
Calculate new vertices:
$$
A' = (1+2, 2-1) = (3,1) \\
B' = (4+2, 2-1) = (6,1) \\
C' = (2+2, 5-1) = (4,4)
$$
3. **Reflect over the y-axis:**
Reflection rule over y-axis: $(x,y) \to (-x,y)$
Apply to translated points:
$$
A'' = (-3,1) \\
B'' = (-6,1) \\
C'' = (-4,4)
$$
4. **Rotate 90 CCW about the origin:**
Rotation rule 90 CCW: $(x,y) \to (-y,x)$
Apply to reflected points:
$$
A''' = (-1,-3) \\
B''' = (-1,-6) \\
C''' = (-4,-4)
$$
5. **Verify correctness:**
- The original points and each transformation step match the calculations.
- The final coordinates after all transformations are $A'''(-1,-3)$, $B'''(-1,-6)$, and $C'''(-4,-4)$.
**Conclusion:** The transformations and coordinates given are correct.