Question

Triangle ABC has its vertices at the following coordinates:

A(-3, 2) B(0, 4) C(-10, 6)

Give the coordinates of the image triangle A'B'C' after a 90° counterclockwise rotation about the origin.

Answer 1

Answer: A'(-2, -3), B'(-4, 0), C'(-6, -10)

Explanation:

To rotate a point (x, y) counterclockwise by 90 degrees about the origin, we can use the following formulas:

x' = -y

y' = x

Let's apply these formulas to each vertex of triangle ABC:

For point A(-3, 2):

x' = -2

y' = -3

So, the coordinates of A' are (-2, -3).

For point B(0, 4):

x' = -4

y' = 0

So, the coordinates of B' are (-4, 0).

For point C(-10, 6):

x' = -6

y' = -10

So, the coordinates of C' are (-6, -10).

Therefore, after a 90° counterclockwise rotation about the origin, the coordinates of the image triangle A'B'C' are A'(-2, -3), B'(-4, 0), and C'(-6, -10).

I hope this helps :)