Question

write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Find original coordinates

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

• For \( F \): From the grid, \( F \) is at \( (-9, 10) \) (since it's 9 units left on the x - axis and 10 units up on the y - axis).
• For \( G \): \( G \) is at \( (-2, 10) \) (2 units left on the x - axis and 10 units up on the y - axis).
• For \( H \): \( H \) is at \( (-8, 1) \) (8 units left on the x - axis and 1 unit up on the y - axis).

Step2: Apply 90° counterclockwise rotation rule

The rule for rotating a point \( (x,y) \) 90° counterclockwise around the origin is \( (x,y)\to(-y,x) \).

For point \( F(-9,10) \):

Using the rotation rule, substitute \( x=-9 \) and \( y = 10 \) into \( (-y,x) \).
We get \( (-10,-9) \).

For point \( G(-2,10) \):

Substitute \( x=-2 \) and \( y = 10 \) into \( (-y,x) \).
We get \( (-10,-2) \).

For point \( H(-8,1) \):

Substitute \( x=-8 \) and \( y = 1 \) into \( (-y,x) \).
We get \( (-1,-8) \).

Answer:

The coordinates of the vertices after a 90° counterclockwise rotation around the origin are \( F'(-10,-9) \), \( G'(-10,-2) \), and \( H'(-1,-8) \).