Scale Drawings & Area
A drawing uses the scale 1 inch = 4 feet. A wall is 3 inches long on the drawing. How long is the actual wall?
12 feet
What does it mean for two figures to be similar?
Their corresponding angles are equal and their corresponding side lengths are proportional.
If two triangles are similar, what can you say about their corresponding angles?
They have equal measures.
What is a translation in geometry?
A slide that moves a figure without turning or flipping it.
What is a reflection in geometry?
A flip of a figure across a line.
A square has sides of 5 cm. Each side is doubled. How many times as large is the new area?
(Hint: Find the original area, then the new area. How many times bigger is the new area?)
4 times
Two similar triangles have corresponding sides of 3 cm and 6 cm. What is the scale factor from the smaller triangle to the larger triangle?
Scale Factor: 2
Two similar triangles have an angle of 65° and another angle of 45°. What is the third angle?
**HINT: What do the interior angles of a triangle ALWAYS add up to?
70°
What does the rule (x, y) → (x + 3, y) do?
Moves every point 3 units to the right.
Point A is at (3, 4). Reflect it across the x-axis. What is the new coordinate?
**Don't forget the point's new name!
A' = (3, -4)
A rectangle on a map is 6 inches long. The scale is 1 inch = 3 feet. What is the actual length?
18 feet
Two similar figures have corresponding sides of 4 and 16. What is the scale factor from the smaller figure to the larger figure?
Scale Factor: 4
A triangle has angles of 40° and 60°. A similar triangle has a corresponding angle to the 40° angle. What is that angle?
40°
Point A is at (2, 5). Translate it 4 units left and 2 units up. What are the new coordinates?
**Don't forget the point's new name!
A' = (-2, 7)
Point B is at (-5, 2). Reflect it across the y-axis. What is the new coordinate?
**Don't forget the point's new name!
B' = (5, 2)
A square has a side length of 4 inches. Its side length is tripled. What is the area of the new square?
144 square inches. The new side is 12 inches, so 12 × 12 = 144.
Two similar triangles have corresponding sides of 5 and 15. If another side of the smaller triangle is 7, what is the corresponding side of the larger triangle?
(HINT: DRAW IT OUT TO SOLVE)
21 units
Two similar triangles have corresponding sides of 6 and 9. A second side in the smaller triangle is 10. Find the corresponding side in the larger triangle.
15 units
Write a translation rule for moving a figure 5 units right and 3 units down.
(x, y) → (x + 5, y − 3)
Reflect point C at (-4, -3) across the x-axis. Then reflect your new point across the y-axis. What is the new coordinate?
C' = (4, 3)
A floor plan uses a scale of 2 inches = 5 feet. A garage measures 8 inches by 6 inches on the plan. What is the actual area of the garage?
100 square feet. The actual dimensions are 20 feet by 15 feet, so 20 × 15 = 300 square feet.
Triangle ABC is similar to triangle DEF. Side AB = 8, side DE = 12, and side BC = 10. What is side EF?
(HINT: DRAW IT OUT TO SOLVE)
15. The scale factor is 12 ÷ 8 = 1.5, so 10 × 1.5 = 15.
Triangle ABC is similar to triangle DEF. Angle A = 50° and angle B = 70°. What are angles D and F?
Angle D = 50° and angle F = 60°. The remaining angle C is 60°, and corresponding angles are equal.
A triangle has vertices A(1, 2), B(3, 2), and C(2, 4).
Translate it using (x, y) → (x − 2, y + 3).
Give all three new coordinates.
A′ = (-1, 5), B′ = (1, 5), C′ = (0, 7).
A triangle has vertices P(2, 3), Q(-1, 4), and R(0, -2). Reflect the triangle across the y-axis. Give all three new coordinates.
P′ = (-2, 3), Q′ = (1, 4), R′ = (0, -2).