An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. Three triangles are plotted on the graph. The first triangle is placed in the first quadrant with vertices marked as closed points at the following coordinates: left parenthesis 3 comma 1 right parenthesis, left parenthesis 3 comma 3 right parenthesis, and left parenthesis 7 comma 1 right parenthesis. The second triangle is placed in the second quadrant with vertices marked as closed points at the following coordinates: left parenthesis negative 1 comma 3 right parenthesis, left parenthesis negative 5 comma 3 right parenthesis, and left parenthesis negative 5 comma 5 right parenthesis. The third triangle is placed in the fourth quadrant with vertices marked as closed points at the following coordinates: left parenthesis 1 comma negative 3 right parenthesis, left parenthesis 1 comma negative 7 right parenthesis, and left parenthesis 3 comma negative 3 right parenthesis. An arrow goes from the point left parenthesis 3 comma 1 right parenthesis to left parenthesis negative 5 comma 3 right parenthesis; an arrow goes from the point left parenthesis 3 comma 3 right parenthesis to left parenthesis negative 5 comma 5 right parenthesis; an arrow goes from left parenthesis 7 comma 1 right parenthesis to left parenthesis negative 1 comma 3 right parenthesis.

Question

Describe the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II to show that the triangles are congruent.
rotation, then translation
rotation, then translation

translation, then reflection
translation, then reflection

translation, then transformation
translation, then transformation

reflection, then translation

Answer 1

To show that the triangles in Quadrant IV and Quadrant II are congruent, the appropriate sequence of steps involves reflecting the triangle and then translating it.

Here's how to describe this sequence of steps:

1. Reflection: Reflect the triangle in Quadrant IV across the y-axis. This reflection will flip the triangle over to Quadrant II, aligning it such that corresponding vertices match up with those of the triangle in Quadrant II.

2. Translation: After the reflection, translate the reflected triangle to match the position of the triangle in Quadrant II. This means moving the reflected triangle horizontally or vertically so that the vertices coincide with the corresponding vertices of the triangle in Quadrant II.

Thus, the correct answer is reflection, then translation.