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Triangle ABC has vertices A(−3, 1), B(−3, 4), and C(−7, 1).



Part A: If ∆ABC is translated according to the rule (x, y) → (x + 4, y − 3) to form ∆A'B'C', how is the translation described with words? (3 points)
Part B: Where are the vertices of ∆A'B'C' located? Show your work or explain your steps. (4 points)
Part C: Triangle A'B'C' is rotated 90° counterclockwise about the origin to form ∆A"B"C". Is ∆ABC congruent to ∆A"B"C"? Give details to support your answer. (3 points)



Answer :

Using translation concepts, it is found that:

a) The triangle was shifted 4 units right and 3 units down.

b) The vertices are given as follows: A'(1,-2), B'(1,1) and C'(-3,-2).

c) Translations and rotations do not change the side lengths of the triangles, just the orientation or position, hence the triangles are congruent.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In item a, we have that:

  • x -> x + 4 means that the triangle was shifted 4 units right.
  • y -> y - 3 means that the triangle was shifted 3 units down.

Hence the triangle was shifted 4 units right and 3 units down.

For item b, the vertices are given as follows:

  • A': (-3 + 4, 1 - 3) = (1,-2).
  • B': (-3 + 4, 4 - 3) = (1,1).
  • C': (-7 + 4, 1 - 3) = (-3,-2).

Hence:

A'(1,-2), B'(1,1) and C'(-3,-2).

For item c, we have that:

Translations and rotations do not change the side lengths of the triangles, just the orientation or position, hence the triangles are congruent.

More can be learned about translation concepts at https://brainly.com/question/18775151

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