Congruent Figures Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.
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 upper A upper B upper C joined by solid lines are upper A is left parenthesis negative 4 comma 5 right parenthesis, upper B is left parenthesis negative 1 comma 3 right parenthesis, and upper C is left parenthesis negative 3 comma 1 right parenthesis. The coordinates for the second triangle upper A prime upper B prime upper C prime joined by dotted lines are as follows: upper A prime at left parenthesis 4 comma 5 right parenthesis, upper B prime at left parenthesis 1 comma 3 right parenthesis, and upper C prime at left parenthesis 3 comma 1 right parenthesis. The coordinates of the plotted points for the third triangle upper A double prime upper B double prime upper C double prime joined by lines made of dashes and dots are as follows: upper A double prime at left parenthesis 1 comma 0 right parenthesis, upper B double prime at left parenthesis negative 2 comma negative 2 right parenthesis, and upper C double prime at left parenthesis 0 comma negative 4 right parenthesis.
How would you describe this series of transformations?
(1 point)
Responses
Since triangles ABC and A′′B"C" do not have the same orientation, they are not congruent.
Since triangles upper A upper B upper C and upper A double prime upper B double prime upper C double prime do not have the same orientation, they are not congruent.
Rotation of 90 degrees clockwise and then reflection across the x-axis shows that triangle ABC is congruent to triangle A′′B"C".
Rotation of 90 degrees clockwise and then reflection across the x -axis shows that triangle upper A upper B upper C is congruent to triangle upper A double prime upper B double prime upper C double prime .
Reflection across the y-axis and then a translation of (−3,−5) shows that triangle ABC is congruent to triangle A′′B"C".
Reflection across the y -axis and then a translation of left parenthesis negative 3 comma negative 5 right parenthesis shows that triangle upper A upper B upper C is congruent to triangle upper A double prime upper B double prime upper C double prime .
Translation of (2,0) and then reflection across the x-axis shows that triangle ABC is congruent to triangle A′′B"
"C".
Translation of (2,0) and then reflection across the x-axis shows that triangle upper A upper B upper C is congruent to triangle upper A double prime upper B double prime upper C double prime.