Question

Question

Use the image to answer the question.

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. Two triangles, upper A upper B upper C and upper E upper G upper H, are plotted on the graph. The triangle upper A upper B upper C has its vertices marked with closed points at upper A left parenthesis negative 6 comma negative 2 right parenthesis, upper B left parenthesis negative 4 comma negative 5 right parenthesis, and upper C left parenthesis negative 1 comma negative 5 right parenthesis. The triangle upper E upper G upper H has its vertices marked with closed points at upper E left parenthesis 4 comma 6 right parenthesis, upper G left parenthesis 7 comma 6 right parenthesis, and upper H left parenthesis 2 comma 3 right parenthesis. In triangle upper E upper G upper H, side upper E upper G is labeled as h, side upper G upper H is labeled as e, and side upper H upper E is labeled as g.

What is the sequence of transformations needed to move triangle ABC
A
B
C
to triangle EGH
E
G
H
to show that the triangles are congruent?

(___,___)

Answer 1

To determine the transformations needed to move triangle ABC to triangle EGH and show that they are congruent, we will identify the necessary steps.

1. Translation: Move the triangle to a new position on the coordinate plane. We can determine the translation vector by finding how far we need to move each vertex of triangle ABC to align it with the corresponding vertex of triangle EGH.

   • For vertex A (-6, -2) to vertex E (4, 6):
     • Change in x: 4 - (-6) = 10
     • Change in y: 6 - (-2) = 8
   • Therefore, we can translate triangle ABC by a vector (10, 8).

2. Rotation: After translating, it may also be necessary to rotate the triangle so that the orientation matches that of triangle EGH. However, based on the coordinates provided, it appears translations alone may suffice, depending on the final positions of the points after translation.

Considering both steps, if the triangles remain with the same orientation after translation, we wouldn’t need any rotation.

Thus, the sequence of transformations needed is:

• Translation by the vector (10, 8).

The final answer is: (Translation: (10, 8))