G8. C14. Rotation and Dilation

14.4 Rotating shapes

CLS Grade 8
C14. Position and Transformation

Multiple Select

What is needed when performing a rotation?

• A center of rotation

• An angle of rotation

• A calculator

• A compass to measure the angle of rotation and position of the points.

Multiple Choice

The clock is going in the __________ direction.

• Clockwise

• Counterclockwise

Multiple Choice

The clock is going in the __________ direction.

• clockwise

• anti-clockwise

Multiple Choice

Triangle B is rotated 90° anti-clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

Multiple Choice

Which way has this F been rotated

• Up

• Across

• Clockwise

• Anit-clockwise

Fill in the Blanks

Use a number to complete this statement.

Rotating 270° clockwise gives the same image as rotating

° anticlockwise.

Multiple Select

Match the description with the graph shown below.  (Hint: There are two correct answers)

• $$90\degree\ clockwise\ rotation$$  

• $$90\degree\ anti-clockwise\ rotation$$  

• $$270\degree\ clockwise\ rotation$$  

• $$270\degree\ anti-clockwise\ rotation$$  

Multiple Choice

The point D was rotated 90° clockwise using the triangle as a centre of rotation.

The new coordinate of D is:

• (0, 4)

• (4, 0)

• (0,- 4)

• (-4,0)

Multiple Choice

Select the image that shows the original green shape rotated through 90° clockwise about the origin.

Multiple Choice

Rotate the point (5,5) around the origin 180 degrees counterclockwise. State the image of the point.

• (5,-5)

• (5,5)

• (-5,5)

• (-5,-5)

Multiple Choice

Rotate the point (-3,-4) around the origin 180 degrees. State the image of the point.

• (-4, -3)

• (-4, 3)

• (4, -3)

• (3, 4)

Multiple Choice

The point B(0, 8) is rotated 90° clockwise about the origin.

What will the coordinates of its image be?

• (8,0)

• (-8,0)

• (0,8)

• (0,-8)

Fill in the Blanks

Give the new coordinates of the point (–4, 2) on the triangle after a rotation of 180°, centre (−1, 2).

Ans : (__ , __)

Fill in the Blanks

Give the new coordinates of the point (3, 4) on the triangle after a rotation of 180°, centre (3, 0).

Ans : (__ , __)

Fill in the Blanks

Give the new coordinates of the point (5, 3) on the triangle after a rotation of 90° clockwise, centre (1, −2).

Fill in the Blanks

Give the new coordinates of the point (5, 3) on the triangle after a rotation of 90° clockwise, centre (1, −2).

Fill in the Blanks

Give the new coordinates of the point (2, 4) after a rotation of 90° anticlockwise, centre (0, 0), followed by a reflection in the x-axis.

14.4 Rotating shapes

CLS Grade 8
C14. Position and Transformation

Scale Factors (k)

k > 1 Enlargement

k > 0 & k < 1 Reduction

k = 0 Makes it a point

k is Negative: Reflection through Point (Center of Dilation)

Multiple Choice

Triangle PQR is similar to triangle DEF shown. Which describes the relationship between the corresponding sides of the two triangles?

Dilations create Similar Figures

• Corresponding angles are congruent

• Corresponding sides are proportional

• Since sides are proportional, we can write an equivalent proportion

Multiple Select

Select all scale factors which would increase an image.

• $$\frac{3}{2}$$

• $$\frac{1}{2}$$

• $$3.5$$

• $$\frac{2}{1}$$

• 5
  

Multiple Choice

If your SF = 0.8, what type of dilation is it?

• Reduction

• Enlargement

Multiple Choice

Does the image show a Dilation? If yes, did the image enlarge, reduce or none of the above?

• Yes, enlarge
• Yes, reduce
• No

Multiple Choice

If your SF = 2.5, what type of dilation is it?

• Reduction

• Enlargement

Multiple Choice

Did the image enlarge, reduce or none of the above?

• Enlarge
• Reduce
• None of the above

Multiple Choice

A(1,2) is a point on a triangle. If the triangle is dilated by a scale factor of k =4, what is the coordinate of A'?

• A' (0.25, 0.5)

• A' (-4, -8)

• A' (4, 8)

Multiple Choice

What is the image of K(6, 8) after a dilation of k = 1/2 ?

• K' (4, 3)

• K' (12, 16)

• K' (3, 4)

Multiple Choice

Dilate Point B by a scale factor of 1/2

• (1.5,-4)
• (-1.5,1)
• (-1,-1.5)
• (-2,-2)

Multiple Choice

Triangle ABC will be dilated by a scale factor of 1/2.  What will be the coordinates of C'?

• (-1, -2.5)
• (12, 6)
• (3, -1.5)
• (0, 1.5)

Dilations also affect perimeter and area!

Make sure to find the perimeter/area before and after the dilation, then compare! It may help to draw a picture!

Multiple Choice

Rectangle ABCD has a length of 6 and a height of 5. It is dilated by a scale factor of 3.

What is true about the perimeter of A'B'C'D', the new rectangle?

• The perimeter of A'B'C'D' is the same as the perimeter of ABCD

• The perimeter of A'B'C'D' is the 3 times larger than the perimeter of ABCD

• The perimeter of A'B'C'D' is the 6 times larger than the perimeter of ABCD

• The perimeter of A'B'C'D' is the 9 times larger than the perimeter of ABCD

Multiple Choice

Jane's garden is a 2 ft x 3 ft rectangle. If she increases it by a scale factor of 3, what is the new area of her garden?

• 72 square feet

• 18 square feet

• 36 square feet

• 54 square feet

Multiple Choice

A triangle has a perimeter of P units. The triangle is dilated by a scale factor of 1/2.

Which expression could represent the perimeter of the new shape?

• $$\frac{1}{4}P$$ units

• $$\frac{1}{2}P$$ units

• 2P units

• 4P units

Multiple Choice

A rectangle is dilated by a scale factor of 2.

What happens to the area?

• doubles

• triples

• quadruples

• not enough information