Start here

You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Now let's plot (-5, 2). The x is -5, so which way do we move? Left 5 units. The y is 2, which is positive, so which way? Up 2 units. Left and up lands us in which quadrant? Quadrant II. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartA rectangle has vertices (1, 1), (7, 1), (7, 4) and (1, 4). How long is the bottom side?

   1. A6 units
   2. B3 units
   3. C8 units
   4. D4 units

   How do you know?
3. 3

   Warm restartUsing that same rectangle — (1, 1), (7, 1), (7, 4), (1, 4) — what is its area?

   1. A18 square units
   2. B9 square units
   3. C18 units
   4. D24 square units

   How do you know?
4. 4

   Warm restartA square has vertices (−2, −2), (2, −2), (2, 2) and (−2, 2). What is its perimeter?

   1. A16 units
   2. B8 units
   3. C16 square units
   4. D4 units

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughWhich quadrant is the library (−3, 4) in?

   1. AQuadrant II
   2. BQuadrant I
   3. CQuadrant III
   4. DQuadrant IV

   Why is that the answer?
2. 6

   Think it throughWhich quadrant is the park (5, −2) in?

   1. AQuadrant IV
   2. BQuadrant I
   3. CQuadrant II
   4. DQuadrant III

   How do you know? Give a second reason as well.
3. 7

   Think it throughWhich location is in Quadrant III?

   1. AThe hospital (−4, −1)
   2. BThe school (2, 3)
   3. CThe library (−3, 4)
   4. DCity Hall (0, 0)

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelHow do the signs of the x- and y-coordinates tell you which quadrant a point is in?

Use the words

Fill each blank with a word from the bank.

• The ___ of a point's two coordinates decide which quadrant it lands in.
• One of the four regions of the coordinate plane, numbered I to IV, is a ___.
• A coordinate less than zero, which places a point left of or below the origin, is a ___.
• A flip of a point over an axis is a ___.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: A common mistake in Ordered Pairs in All Four Quadrants is matching each sign to the wrong axis — for example, seeing (-2, 5) and thinking "the x is negative so I move DOWN, and the y is positive so I move RIGHT," which lands the point in Quadrant IV.
2. 10

   Say morePlot (-3, -4). Which quadrant is it in, and how do the negative coordinates change the directions you move from the origin?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A colorful eight-petaled flower design sits on a coordinate grid. An orange octagon is centered on the origin O, four maroon hexagon petals point straight up, down, left, and right along the axes, and four teal petals fill the space between them.

   Show your work

Last check

These two come from Lesson 7.7. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — A point has a negative x-coordinate and a negative y-coordinate. Which quadrant is it in?

   1. AQuadrant I
   2. BQuadrant II
   3. CQuadrant III
   4. DQuadrant IV

   Explain your choice.
2. 13

   From Lesson 7.7Explain your thinking — A rectangle has vertices (-1, 4), (5, 4), (5, 1), (-1, 1). What is its perimeter?

   1. A18 units
   2. B9 units
   3. C6 units
   4. D18 square units

   How do you know?
3. 14

   From Lesson 7.7The park's length is 800 feet, and each grid unit represents 100 feet. How many units below the known vertices do the new corners sit?

   1. A8 units
   2. B80 units
   3. C800 units
   4. D0.8 units

   How do you know?

Be honest — this tells your teacher what to do next