Checkpoint 3 Review

CHeckpoint 3 REView

• Pythagorean Theorem & The Converse

• Distance Formula

• Volume & Surface Area

• Transformations

• Scatterplots & Predictions

• The Pythagorean Theorem is used to find the missing side of a right triangle.

• When finding c, we add.

• When finding a or b, we subtract.

Pythagorean Theorem

• PLEASE draw a picture when given a word problem.

• Common word problems we talked about: rectangle split diagonally, ladder against a wall, directional problems, etc.

Word Problems

• If the Pythagorean Theorem only works on right triangles, then we can use the Pythagorean Theorem to prove if 3 sides make a right triangle.

Converse

Multiple Choice

What is the length of the missing side?

• x = 4

• x = 8

• x = 10

• x = 16

Multiple Choice

A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew?

• 7.5 in
• 12.4 in
• 13.6 in 
• 14.3 in

Multiple Choice

Does the set of numbers represent a right triangle?

20, 25, 15

• Yes

• No

• Used to find the distance between 2 points (x, y).

• Please label your points before plugging in.

  • ex: (2, 3) and (-4, 8)

How to find the distance between 2 points

• If you are given a line on a graph and asked to find a distance, make it into a triangle and use pythagorean theorem if you would rather!

​​Or you can use pythagorean theorem on a graph

Multiple Choice

Use the Distance Formula to find the distance between:

(-6,-3) and (-4,-8)

• 5.4

• 7.1

• 6.6

• 4.8

Fill in the Blanks

Find the distance between the two points.

Multiple Choice

What is the distance between AB

• 0

• 8

• 9

• 7

• Remember, the order of the numbers being plugged in really doesn't matter.

• You have to use the right formula! And do it correctly.

• Volume is labeled units cubed! Surface area is labeled units squared!

Volume & surface area
tips

• Slides the shape.

• Adds and subtracts to x or y depending on what direction you go.

• x: left (-) right (+)

• y: down (-) up (+)

Translations

• Flips the shape.

• Reflect over the x-axis means opposite of y.

• Reflect over the y-axis means opposite of x.

reflections

• Turns the shape.

• Clockwise = right

• Counterclockwise = left

• 1 quadrant = 90 degrees

• 2 quadrants = 180 degrees

• 3 quadrants = 270 degrees

• 4 quadrants = 360 degrees

rotations

• Changes the size of the shape by multiplying by a scale factor.

• If the scale factor is less then 1, it gets smaller.

• If the scale factor is bigger than 1, it gets bigger.

​​dilations

Multiple Choice

When you translate, (x-4,y) will move _____.

• 4 units right
• 4 units left
• 4 units up
• 4 units down

Multiple Choice

Write a rule for the translation.

•  (x -1, y  + 2)
•  (x -2, y  + 1)
•  (x +2, y  - 1)
• (x +1, y  -  2)

Multiple Choice

Identify the transformation.

• Reflection across y axis
• Reflection across x-axis
• 180 Rotation
• Translation 2 units down

Multiple Choice

If the rectangle were rotated 90º counterclockwise about the origin, what would be the location of K'?

• (1, -6)

• (-1, 6)

• (6, -1)

• (-6, -1)

Multiple Choice

Triangle ABC will be dilated by a scale factor of 1/2.  What will be the coordinates of C'?

• (-1, -2.5)
• (12, 6)
• (3, -1.5)
• (0, 1.5)

• Positive Association: both variables move the same way.

  • Increase, increase

  • Decrease, decrease

• Negative Association: both variables move opposite ways.

  • Increase, decrease

  • Decrease, increase

Association

• When asked to give a prediction from a scatterplot, draw a trend line! Make sure it goes through the middle of all points.

• When asked to predict with an equation, make sure you know whether you are plugging in for x or y. When all of the numbers are on the same side, use PEMDAS. When they are not, use box-split.

Predictions

• If you need to write an equation for a trend line, use y=mx+b.

• m = slope. Use rise/run.

• b = y-intercept. Where the line crosses the y-axis.

• Use counting points on the line to count slope, they do not have to be scatterplot points!

trend lines

Multiple Choice

What type of correlation would you likely see with:

The amount of time spent working compared to the amount of money earned

• positive correlation

• negative correlation

• no correlation

Multiple Choice

As the age of the car increases, its value decreases. Which scatterplot represents this relationship?

• A
• B
• C
• D

Multiple Choice

Which of the following lines represents the line of best fit for the scatter plot?

• A
• B
• C
• D

Multiple Choice

Based on the scatterplot, what is the best prediction of the average number of hours a person spends at work every week, if that person spends an average of 10 hours on recreational activities every week?

• 33 hours
• 85 hours
• 50 hours
• 65 hours

Multiple Choice

For which scatterplot would the line of best fit be represented by the equation:

y=1/2 x +2?