ID: A
Stretching Quiz 1 Study Guide
Answer Section
SHORT ANSWER
1.
a. 12 inches by 15 inches
b. 50%
1
c.
2
d.
The corresponding angles in both photos will have the same measures: all 90°.
e.
Perimeter of original = 36 inches Perimeter of reduced = 18 inches The perimeter of the original is 2
1
times the size of the reduced photo. OR The perimeter of the reduced photo will be the perimeter
2
of the original photo.
f.
Area of original = 80 sq inches Area of reduced = 20 sq inches The area of the original photo is 4
1
times as large as the area of the reduced photo. OR The area of the reduced photo will be the area
4
of the original photo.
1
ID: A
2. a. Area = 24 square units
b. Rectangle EFGH
c. Area = 6 square units
Perimeter = 20 units
Perimeter = 10 units
d. Rectangle JKLM
Point
(2x, 1.5y)
J
K
L
M
e.
(0, 9)
(12, 9)
(12, 3)
(0, 3)
Area = 72 square units Perimeter = 36 units
Rectangle EFGH is similar to Rectangle ABCD, because the corresponding sides differ by the same
1
scale factor, . Since they are both rectangles, the corresponding angles have the same measures,
2
1
90°. The perimeter of Rectangle EFGH is the perimeter of Rectangle ABCD. The area of Rectangle
2
1
EFGH is the area of Rectangle ABCD, so 4 copies of EFGH would fit into ABCD.
4
3. a. The horizontal lengths would increase by a factor of 3, and the vertical lengths would increase by a factor
of 6.
b. The figure would stay the same size, but it would move to the right 2 units and up 1 unit.
c. The figure would increase by a scale factor of 2 and would move up 5 units.
4. a. (2x, 2y)
b. They are similar, because all corresponding sides increased by a scale factor of 2 and corresponding angles
are equal.
5. Sails B, E, G, and H are similar to Gilligan's sail. Possible explanation: The scale factor from Gilligan's sail
1
to sail B is , to sail E is 2, to sail G is 1.5, and to sail H is 1.
3
6. a. Answers will vary. Possible answers: 6 by 8, 9 by 12, 4.5 by 6.
b. Answers will vary. Possible answers: 1.5 by 2, 1 by 1.33.
c. Answers will vary. Possible answer: 3 by 5.
2
ID: A
7.
Angle
A
B
C
D
E
8. a.
b.
9. a.
b.
10. a.
b.
corresponds to
Angle
V
W
X
Y
Z
Side
Side
AB
VW
BC
WX
corresponds to
CD
XY
DE
YZ
EA
ZV
4 copies will fit.
This will be true for any two such squares. Two copies of the smaller square will fit side-by-side in the
larger square. Two of these rows can fit vertically in the larger square, for a total of four squares.
The sides of the original quadrilateral measure 2 cm and 3 cm. The sides of the image measure 0.6 cm and
0.9 cm. 0.6 is 30% of 2 and 0.9 is 30% of 3. Carl entered 30% into the photocopier.
Amy’s image is a quadrilateral similar to the original, with side lengths 5 cm and 7.5 cm.
9 copies will fit.
This will be true for any two such rectangles. Three copies of the smaller rectangle will fit
side-by-side in the larger rectangle. Three of these rows can fit vertically in the larger rectangle, for a
total of nine rectangles.
3