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In this lesson, we will learn how to rotate a shape through 90, 180, and 270 degrees about the origin and investigate what happens to the coordinates as a result.

Q1:

Determine the images of the vertices of triangle π΄ π΅ πΆ after a clockwise rotation of 9 0 β about the origin.

Q2:

Given that π ( 4 , β 2 ) , π ( 8 , β 3 ) , and π ( 5 , β 8 ) form a triangle, determine the images of its vertices after a clockwise rotation of 1 8 0 β about the origin.

Q3:

What is the image of the point ( β 3 , 1 4 ) after a rotation about the origin through an angle of 9 0 β ?

Q4:

What type of transformation is the following?

Q5:

What is the image of π΄ π΅ πΆ π· under the transformation ( π₯ , π¦ ) β ( β π¦ , π₯ ) ?

Q6:

Which transformation can turn the letter d into p?

Q7:

Which transformation can turn the letter Z into N?

Q8:

Which of the following represents a rotation of the shaded figure?

Q9:

A triangle has its vertices at the points (2, 1), (3, 2) and (2, 4). The triangle is rotated 9 0 β counterclockwise about the origin. At which of the following coordinates will the image have its vertices?

Q10:

Rotate the given triangle about the origin 9 0 β clockwise. Which of the following sets of coordinates will be the vertices of the image?

Q11:

Determine the coordinates of the verticesβ images of triangle π΄ π΅ πΆ after a counterclockwise rotation of 1 8 0 β around the origin.

Q12:

Given that π ( 4 , β 4 ) , π ( 8 , β 5 ) , and π ( 5 , β 6 ) , form a triangle, determine the images of its vertices after a clockwise rotation of 9 0 β about the origin.

Q13:

Determine the coordinates of the verticesβ images of triangle π΄ π΅ πΆ after a counterclockwise rotation of 2 7 0 β around the origin.

Q14:

A triangle graphed on the coordinate plane has a vertex at ( 6 , 0 ) . Which of the following rotations would move the vertex to point ( 0 , 6 ) ?

Q15:

The point π΄ ( 3 , 0 ) is rotated about the origin by π degrees. On which of the given figures will the image of π΄ lie?

Q16:

Two points π΄ and π΅ have coordinates ( β 5 , 1 ) and ( β 2 , 1 ) respectively. π΄ π΅ is rotated 2 7 0 β counterclockwise to π΄ β² π΅ β² .

Determine the coordinates of π΄ β² and π΅ β² .

Is the length of π΄ π΅ greater than, less than, or equal to the length of π΄ β² π΅ β² ?

Q17:

Describe the single transformation that would map triangle π΄ π΅ πΆ onto triangle π΄ β² π΅ β² πΆ β² in the given figure.

Q18:

A triangle has vertices at the points seen in the figure. Rotate the triangle 9 0 β counterclockwise about the origin, and determine the coordinates of the image.

Q19:

Rotate triangle π΄ π΅ πΆ 1 8 0 β clockwise about the origin, and state the coordinates of the image.

Q20:

Rotate triangle π΄ π΅ πΆ 9 0 β clockwise about the origin, and state the coordinates of the image.

Q21:

β ο© ο© ο© ο© β π΄ π΅ and β ο© ο© ο© ο© β πΆ π· are parallel. Both have been rotated 9 0 β clockwise about the point πΈ to β ο© ο© ο© ο© ο© ο© ο© β π΄ β² π΅ β² and β ο© ο© ο© ο© ο© ο© ο© ο© β πΆ β² π· β² respectively. What do you notice about β ο© ο© ο© ο© ο© ο© ο© β π΄ β² π΅ β² and β ο© ο© ο© ο© ο© ο© ο© ο© β πΆ β² π· β² ?

Q22:

In the given figure, a rotation of 9 0 β counterclockwise about the point π΅ β² would map triangle π΄ π΅ β² πΆ to triangle π΄ β² π΅ β² πΆ β² . Does it follow that the two triangles are congruent?

Q23:

A rotation about π takes π to π β² and π to π β² . What is the angle of rotation? If π π = 4 5 , what is π π β² ?

Q24:

In the given figure, if π is the midpoint of π΄ π΅ , then π can be rotated 1 8 0 β about π to π . Hence, π and π must be congruent. Is this statement true or false?

Q25:

π΄ π΅ is rotated 9 0 β clockwise about the origin. Is the length of the image resulting from this transformation greater than, less than, or the same as the length of π΄ π΅ ?

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