Math 2: Algebra 2, Geometry and Statistics Ms. …lps.lexingtonma.org/cms/lib2/MA01001631/Centricity/Domain...Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133

Math 2: Algebra 2, Geometry and Statistics

Ms. Sheppard-Brick 617.596.4133 http://lps.lexingtonma.org/Page/2434

Name: Date:

Do Now 21 – Using the Pythagorean Theorem

Danielle measured two of the computer screens in her school’s computer lab. The two screens and some of their dimensions are shown below.

1. What is the area, in square inches, of Screen 1?

2. What is x, the diagonal length in inches of Screen 1? Show or explain how you got your answer.

3. Which computer screen, Screen 1 or Screen 2, has the greater area? Show your work or explain how you got your answer.

Math 2 Week 9 Packet Page 1



Name: Date:

How Far? – An Investigation

Record the names of the people in your group who are filling each role. Facilitator ______________________________ Reader ____________________________________ Technician _______________________________ Encourager _________________________________ Background: Jen is learning geography and cartography (map-‐making). She would like to have a way to calculate how far two places are from each other simply by using their longitude (measures of how far east or west of Greenwich, U.K. they are) and latitude (measures of how far north of south of the equator they are), the grid lines commonly found on maps. To simplify her task, Jen decides that she will begin by modeling the map earth using the coordinate plane. So she must determine how to find out how far apart two points are based on their coordinates. Horizontal Distance Jen begins by looking at two points that have the same y-‐values.

1. Find the distance between each of the following pairs of points.

a. A (1, 4) and B (6, 4) AB (distance from A to B) =

b. C (-‐3, -‐2) and D (-‐7, -‐2) CD =

c. E (-‐4, 3) and F (2, 3) EF =

d. A (2, 3) and B (6, 3)

AB =

e. C (-‐6, -‐2) and D (-‐3, -‐2)

CD =

f. E (-‐4, 5) and F (2, 5) EF =




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She decides to call the x-‐value in the first point x1, and the x-‐value in the second point x2, so her two points are (x1, y) and (x2, y).

2. Assume x1 is larger than x2. Write an expression for the distance from a to x2.

3. Assume x2 is larger than x1. Write an expression for the distance from a to x2.

4. Now assume you don’t know whether x1 or x2 is larger. Write an expression that will work for the distance between points on a horizontal line with any two values.

Jen moves on to vertical lines.

5. Find the distance between each pair of points. Each pair of points is on a vertical line.

a. A(4, 6) and B(4, 1) AB =

b. C (-‐3, -‐6) and D (-‐3, -‐10) CD =

c. E (2, -‐10) and F (2, 1) EF =

6. Using the example above with horizontal lines, what should Jen call the coordinates

of the endpoints of any vertical line?

7. Write expression that will work for the distance between points on a vertical line with any two values.




Name: Date:

Having solved the problem for horizontal and vertical lines, Jen moves on to other lines.

8. Find the distance between each pair of points.

a. G (-‐3, 4) and H (5, -‐2) GH =

b. I (-‐5, -‐3) and J (2, 9) IJ =

c. K (-‐3, 5) and L (1, 9) KL =

d. M (1, -‐10) and N (9, 5) MN =




Name: Date:

Jen wants to find a formula that she can use all the time. She decides to start from a special case.

9. Suppose one point is at (0, 0) and the other point is at (x, y) in the first quadrant (i.e. both x and y are positive)

a. How long would the horizontal base of the right triangle be?

b. How long would the vertical base of the right triangle be?

c. Use your answers to parts a and b to find the distance between (0, 0) and (x, y).

Jen realizes that she actually already knows how to find the length of the horizontal and vertical bases. She just needs to use the expressions she has above and the Pythagorean theorem to find her general distance formula.

10. Use the equation above and your answers to questions 7 and 8 to create a formula for diagonal distance squared. Is there any part of your original formulas that you don’t need now that you are squaring the results?

11. Solve your equation for d. Your result is the distance formula.




Name: Date:

Homework 16 – Using the Distance Formula1

Find the distance between each pair of points. Show your work.

5) (10, 20) and (13, 16) 6) (15, 37) and (42, 73) 7) (-19, -16) and (-3, 14)

1 Adapted from kutasoftware.com and Discovering Geometry © Key Curriculum Press




Name: Date:

8. Find the perimeter of a triangle with vertices A (2, 4), B (8, 12) and C (24, 0) 9. Determine whether triangle DEF with vertices D (6, -6), E (39, -12), and F (24, 18) is scalene, isosceles, or isosceles.




Name: Date:

Do Now 22 – Distance Formula

1. Use the distance formula to find 5 points that are 10 units away from the point (1, 2).

2. Use the distance formula to find 5 points that are 6 units away from the point (3, 4).




Name: Date:

Do Now 23 – Slopes of Perpendicular Lines

Directions: for each of the pairs of lines below:

a. Find the slope of each line (use slope triangles to make it easy) b. Find the product of the slopes of the pair of lines (slope of one line times slope

of the other line) 1.

slope of j = slope of k = product of slopes =

2.

slope of j = slope of m = product of slopes =

3.


4.


Can you make a general statement about the slopes of perpendicular lines?

6

4

2

–2

–4

–6

–10 –5 5

j

k

6

4

2

–2

–4

–6

–10 –5

j

m

6

4

2

–2

–4

–5 5 10

j

m

6

4

2

–2

–4

–5 5 10j

m




Name: Date:

Proving The Perpendicular Lines Slope Theorem




Name: Date:

And the Converse:




Name: Date:

Math 2 Week 9 Assignment Guide

B-‐Block C-‐Block In Class We For Homework

You Should In Class We For Homework

You Should Monday Investigated how

to find the distance between two points (pages 2-‐5 in this packet)

Complete Homework 16 (pages 6-‐7 in this

packet)

Investigated how to find the

distance between two points (pages 2-‐5 in this packet)

Do Homework 16 (pages 6-‐7 in this

packet)

Tuesday Learned and used the midpoint formula (pages 664-‐667 in the 8C textbook packet)

Complete Homework 17:

pages 667-‐668 (in 8c packet) #8, 10, 11, 12, 16, 22. 16a and 16c are

challenge problems.

Wednesday Learned and used the midpoint formula (pages 664-‐667 in the 8C textbook packet)

Complete Homework 17:

pages 667-‐668 (in 8c packet) #8, 10, 11, 12, 16, 22. 16a and 16c are

challenge problems.

Thursday Proved that points were collinear and that lines were

parallel (page 671 #6-‐10)

Complete Homework 18: Page 672 (in the 8C packet) #1, 2,

5, 6, 7

Proved that points were collinear and that lines were

parallel (page 671 #6-‐10)

Complete Homework 18: Page 672 (in the 8C packet) #1, 2,

5, 6, 7 Friday Determined and

proved whether two lines were perpendicular (pages 10-‐11 in this packet & page 676 #9-‐11 and page 677 #1-‐3 in the 8C packet)

Homework 19: Page 677-‐678 in the 8C packet #5,

6, 7, 9.

Determined and proved whether two lines were perpendicular (pages 10-‐11 in this packet & page 676 #9-‐11 and page 677 #1-‐3 in the 8C packet)

Homework 19: Page 677-‐678 in the 8C packet #5,

6, 7, 9.


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Math 2: Algebra 2, Geometry and Statistics Ms. …lps.lexingtonma.org/cms/lib2/MA01001631/Centricity/Domain...Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick 617.596.4133