Slope
Draw a line with a slope of 2/3.
Rise 2 and Run 3.
True or False.
Dilations always keep the angles the same.
True -- when you dilate a figure, the angles will always stay the same.
~ similar
A figure is using a scale factor of 1/2. If a side length was 12 cm, what is the new length?
6 cm
A figure is dilated with a scale factor of 3/2.
Is the image larger, smaller, or the same size as the original?
1.5 times larger than the original figure
What does slope measure on a graph?
How steep a line is (the rate of change).
True or False
Dilations of a line are always parallel to the original line.
True
When given two triangles, how many pairs of angles do you need to prove that they similar?
At least TWO pairs of angles.
Find the scale factor from 15cm to 10cm. (Make sure you simplify if needed.)
10/15 = 2/3
Which transformations are non-rigid, and why?
Dilations, because they change the size of the figure.
Write the slope formula given two points.
(y2 - y1) / (x2 - x1)
A triangle is dilated from the origin using a scale factor of 3. If one vertex is at (2, 1), what are the coordinates of the image?
(6,3)
Two rectangles are similar.
Rectangle A has a length of 6 and a width of 4.
Rectangle B has a length of 9.
What is the width of Rectangle B?
Scale factor = 9 ÷ 6 = 1.5
Width = 4 × 1.5 = 6
A triangle is dilated with a scale factor of 1 from a center of dilation. What happens to the triangle, and why?
The triangle stays the same, because a scale factor of 1 does not change size.
Which statement is always true?
A. Dilations of a triangle keep angle measures the same.
B. Dilations of a triangle keep side lengths the same.
C. Dilations of a triangle must be congruent to the original triangle.
D. Dilations of a triangle always make the sides longer.
A - angles measurements always stay the same when dilating an image; they are similar.
What is the slope of a horizontal line?
zero slope
A square has a vertex at (–4, 2). After a dilation centered at the origin with a scale factor of 2, what are the new coordinates?
(-8,4)
Triangle ABC has angles measuring 30°, 60°, and 90°.
Triangle DEF has angles measuring 30°, 60°, and 90°.
Are the triangles similar? Explain why.
Yes. All corresponding angles are equal, so the triangles are similar by AA similarity.
A map uses a scale where 1 inch represents 25 miles. If two cities are 4 inches apart on the map, how far apart are they in real life?
100 miles
A point (6, 4) is dilated from the origin with a scale factor of 3. What are the new coordinates?
(18, 12)
A car travels 120 miles in 3 hours at a constant rate.
What is the slope, and what does it represent?
Slope = 120 ÷ 3 = 40
It represents 40 miles per hour.
A point is located at (8, −6). It is dilated from the origin using a scale factor of ¾. What are the coordinates of the image?
(6, -4.5)
Two similar triangles have a scale factor of 2 from the smaller triangle to the larger triangle.
If the perimeter of the smaller triangle is 18 units, what is the perimeter of the larger triangle?
36 units
A square has a side length of 6 cm. It is enlarged using a scale factor of 2.5. What is the area of the new square?
225 square centimeters?
(New side length = 15 cm, area = 15 × 15 = 225)
Two rectangles are proportional.
Rectangle A is 8 by 10. Rectangle B has a width of 12.
What is the length of Rectangle B?
Scale factor = 12 ÷ 8 = 1.5
Length = 10 × 1.5 = 15