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.
a. translation, then transformation.
b. translation, then reflection
c. rotation, then translation
d. reflection, then translation
a. translation, then transformation.
b. translation, then reflection
c. rotation, then translation
d. reflection, then translation
Answers
GPT-4o mini
To determine the appropriate sequence of steps to show that the triangles in Quadrant IV and Quadrant II are congruent, let's analyze the positions of the triangles. A triangle in Quadrant IV will have both x-coordinates and y-coordinates that can be negatively oriented, whereas a triangle in Quadrant II will have both x-coordinates negative and y-coordinates positive.
To move the triangle from Quadrant IV to Quadrant II, you would first need to reflect it across the y-axis (to change the x-coordinates from negative to positive), and then possibly translate it vertically if necessary to match y-coordinates.
Given these considerations, the most suitable option from the provided choices is:
**d. reflection, then translation.**
This involves reflecting the triangle to change its position from Quadrant IV to Quadrant II and then translating it vertically if needed to ensure that the triangles align perfectly. This sequence demonstrates that the two triangles are congruent.
To move the triangle from Quadrant IV to Quadrant II, you would first need to reflect it across the y-axis (to change the x-coordinates from negative to positive), and then possibly translate it vertically if necessary to match y-coordinates.
Given these considerations, the most suitable option from the provided choices is:
**d. reflection, then translation.**
This involves reflecting the triangle to change its position from Quadrant IV to Quadrant II and then translating it vertically if needed to ensure that the triangles align perfectly. This sequence demonstrates that the two triangles are congruent.