Quadrant I Triangle : (4, 6) , (7, 6), (2, 3)
Quadrant III Triangle : (-6, -2), (-4, -5), (-1,-5)
What is the sequence of transformations needed to move triangle ABC to triangle EGH to show that the triangles are congruent?
(1 point)
reflection over the x-axis, then a translation of (blank)
To move triangle ABC to triangle EGH, we need to perform the following transformations:
1) Reflection over the x-axis.
After reflecting triangle ABC over the x-axis, we get the new triangle A'B'C' with vertices A' (4, -6), B' (7, -6), and C' (2, -3).
2) Translation.
To translate triangle A'B'C' to triangle EGH, we need to find the vector that represents the translation from A'B'C' to EGH. We can do this by subtracting the coordinates of a corresponding vertex on A'B'C' from the coordinates of the corresponding vertex on EGH. Let's take vertex A' and vertex E as corresponding vertices:
Vector translation = E - A' = (-6, -2) - (4, -6)
= (-6 - 4, -2 - (-6))
= (-10, 4)
Therefore, the sequence of transformations needed is:
Reflection over the x-axis, then a translation of vector (-10, 4).