Question

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Triangle ABC has vertices A(–4,–2), B(–1,3), and C(5,0). Triangle ABC is rotated 180°counterclockwise about the origin to form triangle A′B′C′.


A. What are the coordinates of the vertices of triangle A′B′C′?
B. How could you determine the coordinates of the vertices of the image without using a graph?

Answer 1

Explanation:

check the above images..

Answer 2

Given vertices of the triangle ABC,

A(-4,-2), B(-1,3), and C(5,0),

A) By graphing,

The vertices of preimage of the vertices of A, B and C are shown as below.

B) Since, the rule of 180°counterclockwise about the origin,

`(x,y)\rightarrow (-x, -y)`

If the triangle ABC is rotated 180°counterclockwise about the origin to form triangle A′B′C′.

The vertices of A'B'C' are,

A'(4,2), B'(1, -3), C'(-5,0)