Coordinate Plane
Scale Factor
Center of Dilation
Similarity
Slope & Similar Triangles
100
Draw an example of a coordinate plane with both axes and the origin.
100
What is scale factor?
It is the ratio which tells you how much smaller or bigger an object is than an original.
100
What always comes from the center of dilation?
rays
100
What things are the same between similar figures?
angle measures
100
Slope is a ratio which describes:
a)steepness
b)creepiness
c)sleepiness
a)steepness
200
How many numbers are there in a coordinate point?
2
200
I have a rectangle with height 5. I make a dilated version with scale factor 4. What is the height of the new rectangle?
20 (4x5=20)
200
If a scale factor is greater than 1, will the dilated point be closer or farther from the center than the original point?
farther.
200
If two shapes are similar, their side lengths are related by what?
a ratio, also known as the scale factor
200
How do you calculate slope?
rise/run, change in y over change in x
300
In the point (4,3), what does the number 4 represent?
The horizontal distance from the origin. 4 means it is four units to the right on the x axis.
300
You are making a scale model of the Empire State Building. If the Empire State Building is 1000 feet tall, what scale factor do I need to make a model with height 1 foot?
1/1000th.
300
If a scale factor is less than 1, will the dilated point be closer or farther from the center than the original point?
closer
300
What is the main difference between similarity and congruence?
Congruence means that shapes are exactly the same (sides and angles). Similarity means that shapes have sides related by SF and angles which are the same.
300
What is the slope of this line?
1/2
rise=3-0=3
run=8-2=6
slope = rise/run=3/6=1/2
400
In the point (4,3), what does the number 3 represent?
It represents the distance from the origin in the vertical direction. 3 means it is 3 units up from the origin.
400
I have a square with side lengths 5. I dilate it by scale factor 2 to make a new square. What are the perimeters of both squares?
20 (5+5+5+5=20)
40 (5x2=10, 10+10+10+10=40)
400
What are the coordinates of the center of dilation?
(0,0)
400
Which 3 transformations give congruence and which 1 gives similarity?
Congruence = translations, reflections, rotations
Similarity = dilations
400
What is the slope of this line?
1/2
rise=2-0=2
run=0-(-4)=4
slope = rise/run=2/4=1/2
500
Draw a coordinate plane, label the axes, and label the quadrants!
500
I have a square with side lengths 5. I dilate it by a scale factor 2 to make a new square. What are the areas of both squares?
25 (5x5=25)
100 (5x2=10, 10x10=100)
500
What are the coordinates of the center of dilation?
(-4,-5)
500
Find X.
x=14
First find scale factor (16/24 = 2/3)
Then multiply SF by side corresponding to x.
500
Are triangles A,B, and C similar? Explain how you know.
They are similar. Proven by either:
1. AA
2. Similarity by dilation.
3. Similarity by having the same slope (same ratio of height to width).