Question

graph the image of kite tuvw after a rotation 270° counterclockwise around the origin.

Explanation:

Step1: Identify coordinates of vertices

First, find the coordinates of each vertex of kite \( TUVW \):

• \( W \): \( (0, -5) \) (on the y - axis, 5 units down from origin)
• \( T \): \( (8, -8) \)
• \( U \): \( (9, -6) \)
• \( V \): \( (8, -3) \)

Step2: Apply 270° counterclockwise rotation rule

The rule for a \( 270^{\circ} \) counterclockwise rotation about the origin is \( (x,y)\to(y, - x) \).

• For \( W(0, - 5) \):

Using the rule \( (x,y)\to(y, - x) \), substitute \( x = 0 \), \( y=-5 \). We get \( (-5,0) \) (since \( y=-5 \), \( -x = 0 \))

• For \( T(8, - 8) \):

Substitute \( x = 8 \), \( y = - 8 \) into the rule. We have \( (-8,-8) \) (because \( y=-8 \), \( -x=-8 \))

• For \( U(9, - 6) \):

Substitute \( x = 9 \), \( y=-6 \) into the rule. We get \( (-6,-9) \) (since \( y = - 6 \), \( -x=-9 \))

• For \( V(8, - 3) \):

Substitute \( x = 8 \), \( y=-3 \) into the rule. We have \( (-3,-8) \) (because \( y=-3 \), \( -x = - 8 \))

Step3: Plot the new points

Plot the points \( W'(-5,0) \), \( T'(-8,-8) \), \( U'(-6,-9) \), \( V'(-3,-8) \) on the coordinate plane and connect them to form the image of the kite after rotation.

Answer:

The image of kite \( TUVW \) after a \( 270^{\circ} \) counterclockwise rotation about the origin has vertices at \( W'(-5,0) \), \( T'(-8,-8) \), \( U'(-6,-9) \), and \( V'(-3,-8) \). (The final answer is the set of these rotated points which can be used to graph the image.)