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Session 7:
Homework
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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.
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Problem H1 |  |
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? |
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Problem H2 | |
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? |
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Problem H3 | |
Copy and complete the table below:
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. |
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Problem H4 | |
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.) |
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Problem H5 | |
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.) |
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Problem H6 | |
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.) |
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