-Triangle ABC lies on the
coordinate plane with vertices
located at A (8,6), B (2,-5), and
C (-5, 1). The triangle is
< transformed using the rule
(x,y) - (x + 3,2y) to create
triangle A'B'C'.
Determine the coordinates of
triangle A'B'C'.

Using translation concepts, the coordinates of triangle A'B'C' are given as follows:

A' (11, 12), B' (5,-10), C (-2, 2).

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 range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.

For this problem, the translation rule is given as follows:

(x,y) -> (x + 3, 2y).

Applying the rule to each vertex, we have that:

• A': (8 + 3, 2(6)) = (11, 12).

• B': (2 + 3, 2(-5)) = (5, -10).

• C': (-5 + 3, 2(1)) = (-2, 2).

Hence the coordinates of triangle A'B'C' are given as follows:

A' (11, 12), B' (5,-10), C (-2, 2).

More can be learned about translation concepts at brainly.com/question/4521517

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Final answer:

The transformed coordinates of triangle ABC using the rule (x,y) - (x + 3,2y) are A' (11,12), B' (5,-10), and C' (-2,2).

Explanation:

To solve the problem, we apply the given transformation rule (x,y) - (x + 3,2y) to each vertex of triangle ABC. Thus, vertex A (8,6) will transform into A' (8+3,2*6), B (2,-5) will become B' (2+3,2*-5), and C (-5,1) will transform into C' (-5+3,2*1). Let's calculate:

A'(8+3, 2*6) = A' (11,12). B' (2+3, 2*-5) = B' (5,-10). C' (-5+3, 2*1) = C' (-2,2)

So, the coordinates of triangle A'B'C' after the transformation are A'B'C': A' (11,12), B' (5,-10), C' (-2,2).

Learn more about Coordinate Transformation here:

brainly.com/question/34604852