A coordinate plane with 4 quadrants shows x and y axes ranging from negative 6 to 6 in increments of 1. Three triangles are formed by joining three plotted points each.
The coordinates of the plotted points for the first triangle ABC joined by solid lines are as follows: A is (-4, 5), B is (-1, 3), and C is (-3, 1).
The coordinates for the second triangle A'B'C' joined by dotted lines are as follows: A' at (4, 5), B' at (1, 3), and C' at (3, 1).
The coordinates of the plotted points for the third triangle A"B"C" joined by lines made of dashes and dots are as follows: A" at (1, 0), B" at (-2, -2), C" at (0, -4).
To visualize the triangles on the coordinate plane, plot the points A(-4, 5), B(-1, 3), C(-3, 1), A'(4, 5), B'(1, 3), C'(3, 1), A"(1, 0), B"(-2, -2), C"(0, -4) and then join the points as described above to form the three triangles.
Triangle ABC is formed by joining points A, B, and C with solid lines.
Triangle A'B'C' is formed by joining points A', B', and C' with dotted lines.
Triangle A"B"C" is formed by joining points A", B", and C" with lines made of dashes and dots.
This way, you can visually see how the three triangles are positioned in the coordinate plane.
How would you describe this series of transformations?
The series of transformations can be described as a combination of translations and reflections across the x-axis.
1. Triangle ABC: This is the original triangle with vertices A(-4, 5), B(-1, 3), and C(-3, 1).
- Triangle A'B'C': This triangle is formed by translating ABC to the right by 8 units (A to A', B to B', C to C'), resulting in A'(4, 5), B'(1, 3), and C'(3, 1).
- Triangle A"B"C": This triangle is formed by reflecting ABC across the x-axis. The new triangle A"B"C" has vertices A"(1, 0), B"(-2, -2), and C"(0, -4).
Therefore, the transformations involved are translation and reflection across the x-axis.
choose an answer
Rotation of 90 degrees clockwise and then reflection across the x-axis shows that triangle ABC is congruent to triangle A′′B"C".
Since triangles ABC and A′′B"C" do not have the same orientation, they are not congruent.
Translation of (2,0) and then reflection across the x-axis shows that triangle ABC is congruent to triangle A′′B"C".
Reflection across the y-axis and then a translation of (−3,−5) shows that triangle ABC is congruent to triangle A′′B"C".
The correct answer is:
Translation of (2,0) and then reflection across the x-axis shows that triangle ABC is congruent to triangle A′′B"C".