Question

write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of points \( F \), \( G \), and \( H \) from the graph.

• For point \( F \): Looking at the grid, it is at \( (5, 3) \).
• For point \( G \): It is at \( (5, 4) \).
• For point \( H \): It is at \( (3, 2) \).

Step2: Apply 270° counterclockwise rotation rule

The rule for a \( 270^\circ \) counterclockwise rotation around the origin is \( (x, y)
ightarrow (y, -x) \).

For point \( F(5, 3) \):

Using the rule \( (x, y)
ightarrow (y, -x) \), substitute \( x = 5 \) and \( y = 3 \).
So, the new coordinates \( F' \) will be \( (3, -5) \).

For point \( G(5, 4) \):

Substitute \( x = 5 \) and \( y = 4 \) into the rule \( (x, y)
ightarrow (y, -x) \).
The new coordinates \( G' \) will be \( (4, -5) \).

For point \( H(3, 2) \):

Substitute \( x = 3 \) and \( y = 2 \) into the rule \( (x, y)
ightarrow (y, -x) \).
The new coordinates \( H' \) will be \( (2, -3) \).

Answer:

\( F'(3, -5) \), \( G'(4, -5) \), \( H'(2, -3) \)