Question

Triangle ABC with coordinates A(1,2), B(4,6), C(-1,3) is transformed to create triangle A'B'C' with the transformation indicated:

Translation: (x, y) + (x - 1, 4 - 5)
Provide the image coordinates after the triangle is transformed, i.e., A'B'C'.
a) (2, 7), (5, 11), (0, 8)
b) (2, -3), (5, 1), (0, -2)
c) (0, 7), (3, 11), (-2, 8)
d) (0, -3), (3, 1), (-2, -2)

Answer 1

After applying the given translation, the transformed vertices A'B'C' are:

A'(1, 1), B'(7, 5), C'(-3, 2)

How to apply the transformation

The translation transformation indicated is:

`(x,y)\rightarrow(x+(x-1),y+(4-5)).`

Let's apply this transformation to each vertex of triangle ABC:

Given vertices:

A(1, 2), B(4, 6), C(-1, 3)

Transformation:

A'(x', y') = (x + (x - 1), y + (4 - 5))

For A(1, 2):

A'(x', y') = (1 + (1 - 1), 2 + (4 - 5)) = (1 + 0, 2 - 1)

= (1, 1)

For B(4, 6):

B'(x', y') = (4 + (4 - 1), 6 + (4 - 5))

= (4 + 3, 6 - 1) = (7, 5)

For C(-1, 3):

C'(x', y') = (-1 + (-1 - 1), 3 + (4 - 5))

= (-1 - 2, 3 - 1) = (-3, 2)

Therefore, after applying the given translation, the transformed vertices A'B'C' are:

A'(1, 1), B'(7, 5), C'(-3, 2)

The answer that matches these coordinates is not among the options provided.