Question

unit 7: similarity and transformations

1. a rectangle has length 6 cm and width 4 cm.

the rectangle is to be enlarged by a scale factor of 8.
calculate the length of the enlargement.
a. 80 cm b. 48 cm c. 32 cm d. 14 cm

1. a square frame is projected onto a screen using an overhead projector.

the original square frame has side length 8.5 cm.
the square frame is enlarged by a scale factor of 6.2.
determine the side length of the square frame on the screen.
a. 14.7 cm b. 52.7 cm c. 105.4 cm d. 210.8 cm

1. which example shows a reflection of triangle x in the dotted line?

example i example ii
example iii example iv
a. example iii
b. example i
c. example ii
d. example iv
questions i should practice:

Explanation:

Question 20

Step1: Recall the scale factor formula

To find the length after enlargement, we use the formula: New length = Original length × Scale factor.
The original length of the rectangle is 6 cm, and the scale factor is 8.

Step2: Calculate the new length

New length = \( 6 \times 8 = 48 \) cm.

Step1: Recall the scale factor formula

To find the side length after enlargement, we use the formula: New side length = Original side length × Scale factor.
The original side length of the square is 8.5 cm, and the scale factor is 6.2.

Step2: Calculate the new side length

New side length = \( 8.5 \times 6.2 = 52.7 \) cm.

A reflection over a dotted line (axis of reflection) should result in a mirror image where each point of the original triangle (triangle X) has a corresponding point on the other side of the dotted line, equidistant from the line.

• Example i: The triangle does not appear to be a mirror image across the dotted line (the orientation and position do not match reflection).
• Example ii: The two triangles (original X and the other) are mirror images across the dotted line (the dotted line is between them, and they are symmetric with respect to it).
• Example iii: The figure looks like a parallelogram - related transformation (maybe translation or rotation - not reflection).
• Example iv: The triangle’s orientation and position do not show a mirror image across the dotted line.

So Example ii shows the reflection.

Answer:

b. 48 cm

Question 21