Dilations in Real Life
Please provide 3 examples of where someone may see dilations in real life
Eyes, toy vehicles, babies/parents, model houses, etc.
Apply a scale factor of 2, to these points. Must get all the points correct for full credit
A (1,1)
B (3,3)
C (4,5)
D (8,9)
A' (2,2)
B' (6,6)
C' (8,10)
D' (16,18)
Please define enlargement and reduction.
Enlargement - a geometric transformation that increases the size of a figure proportionally while maintaining its original shape and angle measures
Reduction - geometric transformation that shrinks a figure to a smaller size while maintaining its original shape and proportions
What sports does Ms. Sellers coach?
JH Volleyball and HS Softball
Knox has a toy Grave Digger monster truck. It is a 1:24 scale replica of the real Grave Digger. Is his toy a reduction or an enlargement of the real Grave Digger? What does 1:24 (1/24) scale mean?
Knox's toy is a reduction. 1:24 means 1 unit of measurement (inch or cm) on the model represents 24 of the same units on the real item.
What happens if the scale factor is greater than 1?
Ex: 10, 25, 100
What happens if the scale factor is less than 1?
Ex: 1/2, 1/5, 1/10
If it is greater than 1, the size of the shape will increase. If it is less than 1, the size of the shape will decrease
What is the definition of dilation? Specifically need what it is, and how it impacts the image compared to the original.
(Off front page of notes)
What is the highest scoring game in NBA history?
100 points by Wilt Chamberlain on March 2, 1962. There is a famous photo of him holding a paper with 100 written on it.
What are some tools in real life people can use to provide enlargements and reductions?
Need at least 2 of each.
Enlargement - magnifying glass, camera zoom in, microscope, projector, etc.
Reduction - models, drawings, 3D printings, simulations, etc.
A model airplane is about 2.08 feet long, and 0.55 feet tall. The actual airplane is 250 feet long, and 66 feet tall. What is the scale factor of the model airplane to the nearest whole number?
1/120 or 120th the size of the actual.
How? 250 / 2.08 = 120.19, 66 / 0.55 =120
It is 120th the size of the actual. 1 feet
What is a rigid motion? What are the 3 examples of rigid motions we have learned about?
A transformation that moves a figure that keeps its exact size, shape, side lengths, and angle measures. It changes only the position or orientation of an object—such as sliding, flipping, or rotating—resulting in an image that is congruent to the pre-image.
3 examples are translation, reflection, rotation
What colors are in the Olympic logo rings? Need all of them for the points.
Blue, Red, Yellow, Green, Black
In art class you are asked to draw a model of your house. Your model is going to be 1:50 scale of your actual house. The dimensions of your house are as followed.
Height: 25 feet, Length:50 feet, Width: 100 Feet
What will the height, length, and width be of your art project?
Height: 0.5 feet (6 inches)
Length: 1 feet (12 inches)
Width: 2 feet (24 inches)
How? Original value / 50 = model size.
A rectangle has side lengths of 12 and 24 units. If the scale factor is 1/3, what will the new rectangle side lengths be?
4 and 8 units.
12 / 3 = 4 OR 12 * 1/3 = 4
24 / 3 = 8 OR 24 * 1/3 = 8
Why is a dilation NOT a rigid motion?
It changes the size of a figure (making it bigger or smaller) while keeping its shape the same. Because distances between points on the figure increase or decrease, it's not "rigid" in the sense of keeping everything the same, only proportional.
What does "love" mean in tennis?
Ex: 15 - love
Zero points or 15 - 0 in the example
The model of Wrigley Field (where the Cubs play) that I have has an outfield wall 0.46 feet high. If the box says this is a 1:25 model of Wrigley Field, how tall are the outfield walls at the real Wrigley Field, to the nearest tenth.
The walls at the real Wrigley Field are 11.5 feet tall.
0.46 * 25 = 11.5 feet.
We know it should be a larger number because the real Wrigley is larger than my model.
Find the new points using a scale factor of 3/2, answers to the nearest tenth. Must get all of them correct.
A (-2,2)
B (-2,3)
C (2,0)
D (1,-2)
A' (-3,3)
B' (-3,4.5)
C' (3,0)
D' (1.5,3)
How? Multiply each value by 3/2 or divide by 2/3
Define scale factor.
The scale factor is the ratio of corresponding side lengths between an image and its pre-image. It determines how much it is reduced or enlarged by. It is the multiplier for coordinates, keeping the shape similar but changing the size.
Who is the Forreston Boys Basketball all time leading scorer (most points in a career)?
Mr. Schneiderman, who scored 1753 points.