Section A Practice Problems

Problem 1

4 shapes on grid. All have 2 sets of parallel sides. B and C each have 4 right angles. B, 3 by 5. C, 3 by 3. Diagonals of A, 2 and 4. D, base, 5, height, 3.

Which shapes are rectangles? ________________________
Which shapes are rhombuses? ________________________
Which shapes are squares? ________________________

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Solution

B and C
A and C
C

Problem 2

lines M and N. Intersected by lines L and K.

Name 2 lines in the diagram that are parallel. ___________________
Name 2 lines in the diagram that are perpendicular. ___________________

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Solution

M and N
L and M or L and N

Problem 3

Draw a rectangle on the grid.
What is the perimeter of the rectangle?

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Solution

Sample response:

28 units

Problem 4

Which triangles are right triangles?

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Solution

A, C

Problem 5

How would you describe point $P$ ?
How would you describe Rectangle R?

Coordinate plane. Rectangle R, 0 comma 2, 0 comma 5, 7 comma 2, 7 comma 5. Point, P, 8 comma 9.

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Solution

Sample responses:

It is over 8 and up 9.
The vertical sides go from 2 and 5 and the horizontal sides go from 0 to 7.

Problem 6

What are the coordinates of the point plotted on this coordinate grid?
Plot and label point $A$ with coordinates $(7, 1)$ , point $B$ with coordinates $(2, 8)$ , and point $C$ with coordinates $(6, 6)$ .

Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's. Point graphed at 9 comma 3.

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Solution

$(9, 3)$

Problem 7

Fill in the blanks with 4 different numbers between 0 and 10 to complete the coordinates for 4 points. Then plot the points on the coordinate grid.

$(\underline{\hspace{1 cm}},0)$ $(\underline{\hspace{1 cm}},0)$

$(\underline{\hspace{1 cm}},0)$ $(\underline{\hspace{1 cm}},0)$

What do you notice about the points?
Plot points at $(1,1)$ , $(2,2)$ , $(3,3)$ , and $(4,4)$ on the coordinate grid. What do you notice about the points?

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Solution

Sample responses:

The points $(1,0)$ , $(4,0)$ , $(6,0)$ , and $(8,0)$ are all on the line at the bottom of the graph, the horizontal axis.
They are all on a line that goes from the bottom left to the top right of the graph.

Problem 8

A student describes the first letter of their name like this: “On a coordinate grid, start at $(2,4)$ and go to $(2,8)$ , then go to $(3,6)$ . Then go to $(4,8)$ , and then to $(4,4)$ .”

Which student is it: Andre, Clare, Diego, Elena, Han, Jada, Kiran, Lin, Mai, Noah, Priya, or Tyler?
Describe, using coordinates, how to trace a letter from your name.

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Solution

Sample response:

Mai. Sample response: I connected the points and got an M. So, it's Mai.
Sample response: (for W) Start at $(0,8)$ then go to $(2,0)$ , then to $(4,5)$ , then to $(6,0)$ , then to $(8,8)$ .

Problem 9

Work with a partner.

Partner A:

Draw a rectangle on the coordinate grid. Make sure the area of the rectangle is at least 20 square units. Don't show the rectangle to your partner.

Coordinate grid. horizontal and vertical axis, 0 to 10, by 1's.

Partner B:

Your goal is to figure out what rectangle your partner drew using the fewest points. Use coordinates to name points in the coordinate grid. Your partner will tell you whether the point is or is not on their rectangle.

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Solution

Sample response:

Points:

$(0,0)$ no

$(1,1)$ no

$(2,2)$ no

$(3,3)$ yes

$(4,3)$ yes

$(5,3)$ yes

$(6,3)$ yes

$(7,3)$ yes

$(8,3)$ no

$(2,3)$ yes

$(1,3)$ yes

$(0,3)$ yes

$(0,2)$ no

$(0,4)$ yes

$(0,5)$ yes

$(0,6)$ yes

$(0,7)$ no

I have a horizontal and vertical side of the rectangle so I know that it goes from $(0,3)$ in the bottom left to $(7,6)$ in the top right.