Dilation
Triangle ABC has vertices:
The triangle is dilated by a scale factor of 2, centered at the origin.
What are the coordinates of A′, B′, and C′?
A′(4, 4), B′(8, 4), C′(4, 12)
Two triangles have the following angle measures:
Triangle A: 40°, 60°, 80°
Triangle B: 40°, 60°, 80°
Must the triangles be similar? Explain.
Yes, because they have the same angle measurements
Find the slope of the line passing through:
(2,3) nd (6,11)
8/4
OR 4/2
Or 2/1
OR 2
For the line
y=3x+5
What is the Y intercept?
Write your answer as a coordinate pair (x, y)
(0, 5)
Write the equation of a line with slope 3 and y-intercept −2.
Y = 3x + -2
Point P(6, 8) is dilated from the origin to P′(3, 4).
What is the scale factor?
1/2
Rectangle A measures 4 by 6. Rectangle B measures 8 by 12.
Are the rectangles similar? Explain how you know.
Or Rectangle B is dilated by a scale factor of 1/2 to be similar, Rectangle A
Find the slope of the line passing through:
(-2,5) and (4,-1)
-6/6
Or 6/-6
Or -1/1
Or -1
A line passes through the origin and has a slope of −3.
What is its y-intercept?
Write your answer as a coordinate pair (x, y)
(0, 0)
(If it passes through the Origin that is where it crosses the Y axis)
Write the equation of a line passing through:
(2,5) and (4,9)
Y = 2x + 1
OR
Y = 4/2 x + 1
A figure is dilated by a scale factor of 1/3
Which statement must be true?
A. The image is three times larger.
B. The image is smaller than the original.
C. The image is congruent to the original.
D. The image changes shape.
B. The image is smaller than the original
Two distinct lines in different locations, with the same slope are parallel.
Is this always, sometimes, or never true? Explain.
Yes, If they have the same slope they will be parallel to each other
A negative slope like -1/4 or -2/3, from left to right which directions will it go (up, down, left, right)
From left to right a negative slope would go down to the right \
A line has a slope of 2 and passes through the point (3, 10).
Write the equation of the line. What is its y-intercept?
Write the equation of the line in Y=mx + b form
Write the Y intercept as a coordinate pair (x, y)
Y = 2x + 4
The Y intercept is (0, 4)
A line passes through (0,4) and (2,10).
Write its equation in slope-intercept form.
Y = 3x + 4
OR
Y = 6/2 x + 4
A triangle has side lengths 4, 6, and 8 units. It is dilated by a scale factor of 1.5.
What are the new side lengths, and what happens to the perimeter?
New side lengths are: 6, 9, 12
Two similar triangles have corresponding side lengths of 8 and 12.
The smaller triangle has another side of length 10.
What is the corresponding side length of the larger triangle?
The larger triangle would have a corresponding side length of 15 because the scale factor is 1.5.
What are two ways we can find the slope?
1. Graph the line from at least 2 points and count our rise and run. (For example: 3 up and 4 to the right would be a slope of 3/4)
2. Assign two coordinates from the line to be coordinate 1 and coordinate 2. The calculate (y2 - y1 is the rise, x2 - x1 is the run)
Line A: (y=3x+4)
Line B: (y=3x-2)
How do the y-intercepts compare? What does this tell you about the graphs?
Line A crosses the Y axis 6 units higher at (0, 4) than Line B at (0, -2)
Line A and B have the same slope so they will be Parallel to each other but line A will always be 6 units higher than B.
A line passes through (1,4) and (-3,10).
Find the slope and write the equation of the line.
Y = - 3/2 x + 11/2
OR
Y = - 3/2 x + 5.5
A triangle is dilated by a scale factor of 3. Its original area is 12 square units.
What is the area of the dilated triangle?
108 square units
Two quadrilaterals have the same angles, but their corresponding sides are not proportional.
Are the quadrilaterals similar? Explain.
NO, the quadrilaterals are not similar because they would need to have proportional relationships between their corresponding side lengths.
Line A has a slope of 3 /4.
Line B passes through (0,2) and (4,5)
Which line is steeper? Explain.
The two lines have the same slope 3/4. Neither one is steeper than the other one.
A line passes through the points (2, 9) and (4, 15).
Find the slope, and identify the y-intercept.
Y = 3x + 3
The slope is 6/2 or 3/1 or 3
The Y intercept is (0, 3)
A taxi charges a $4 starting fee plus $2 per mile.
Y = 2x + 4
Slope is the $2 per mile cost goes up $2 for every mile driven. (cost per mile)
Y intercept is the starting fee. Before you even go 1 mile it costs you $4