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Session 7:
Homework

The coordinate geometry that you first worked with in Session 6 is useful for describing transformations. Before looking at how that works, here are a few problems with coordinates to get you warmed up.

Problem H1

Solution  

Do each part on a new set of axes.

a. 

Find three different points with x-coordinate 0. Where are all the points with x-coordinate 0?

b. 

On a new set of axes, plot the point (1,1). Then draw a horizontal line through that point. Name three other points on that line. What do all the points on that line have in common?

c. 

Suppose v is the vertical line passing the point (3,7). Find the coordinates of three points that are on the line v and three points that are not on the line v. How can you tell if a point is on line v just by looking at the coordinates?

d. 

What are the coordinates of the intersection of the horizontal line through (5,2) and the vertical line through (-4,3)?

e. 

Name and plot five points whose first coordinate is the same as the second coordinate. Where are all such points?


 

Problem H2

Solution  

In this picture, k and m are horizontal lines.

a. 

Find the coordinates of six points between the lines k and m.

b. 

Find the coordinates of six points that are not between the lines k and m.

c. 

How can you tell if a point is between the lines k and m by looking at its coordinates?


 

Problem H3

Solution  

Copy and complete the table below:

A

B

C

D

E

F

G

(x,y)

(x + 3,
y - 2)

(-x,y)

(2x,2y)

(x - 1,
y + 2)

(y,-x)

(2,1)

(1,-2)

(-4,0)

(-1,-2)

(-5,4)

(-4,-5)

a. 

On a piece of graph paper, plot the three points in column A. Connect them to form a triangle. Plot the three points in column B. Connect them to form a triangle. Describe how the two triangles are related.

b. 

On a new piece of graph paper, plot triangles A and C. Describe how they're related.

c. 

Repeat the process for triangles A and D.

d. 

Repeat the same for the rest of the table.


 

Problem H4

Solution  

Start with any point (x,y). Reflect that point over the x-axis. What are the coordinates of the new point? How do they relate to the coordinates of the original point? Explain. (You may want to try several cases.)


 

Problem H5

Solution  

Start with any point (x,y). Reflect that point over the y-axis. What are the coordinates of the new point? How do they relate to the coordinates of the original point? Explain. (You may want to try several cases.)


 

Problem H6

Solution  

Start with any point (x,y). Reflect that point over the line y = x. What are the coordinates of the new point? How do they relate to the coordinates of the original point? Explain. (You may want to try several cases.)


Suggested Reading:

Crowe, D. and Thompson, Thomas M. (Reston, VA: National Council of Teachers of Mathematics, 1987). Transformation Geometry and Archaeology. Learning and Teaching Geometry, K-12, 1987 Yearbook. Edited by Mary Montgomery Lindquist.
Reproduced with permission from the publisher. Copyright © 1987 by the National Council of Teachers of Mathematics. All rights reserved.

Download PDF File:
Transformation Geometry and Archaeology


Next > Session 8: Similarity

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