What is the sequence of transformations needed to move triangle abc to triangle egh to show that the triangles are congruent?
Reflect over the x-axis then translate to coordinate 1
The locations of the triangle in the third quadrant are
A(-6, -2) B(-4, -5) C(-1, -5)
And the ones in the first quadrant are
E(4,6) H(2,3) G(7,6)
The sequence of transformations needed to move triangle ABC to triangle EGH to show that the triangles are congruent is as follows:
1. Reflect triangle ABC over the x-axis:
- Reflect point A(-6, -2) to its image E(6, 2)
- Reflect point B(-4, -5) to its image H(4, 5)
- Reflect point C(-1, -5) to its image G(1, 5)
2. Translate the reflected triangle to coordinate 1:
- Translate point E(6, 2) by subtracting 5 from the x-coordinate and subtracting 1 from the y-coordinate: E(6-5, 2-1) = E(1, 1)
- Translate point H(4, 5) by subtracting 5 from the x-coordinate and subtracting 1 from the y-coordinate: H(4-5, 5-1) = H(-1, 4)
- Translate point G(1, 5) by subtracting 5 from the x-coordinate and subtracting 1 from the y-coordinate: G(1-5, 5-1) = G(-4, 4)
Therefore, reflecting triangle ABC over the x-axis and then translating it to coordinate 1 results in triangle EGH.