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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.

   Let's do one together: The rectangle with vertices (−4.5, 3), (5, 3), (5, −3.75) and (−4.5, −3.75) has sides of 9.5 and 6.75 units. Find its perimeter. How many sides are 9.5 units? How many are 6.75 units? (Two of each. Opposite sides of a rectangle match.) Multiply each length by 2. Then add. (2 × 9.5 + 2 × 6.75 = 19 + 13.5 = 32.5) Why do we multiply each length by 2? (Each length appears on two sides of the rectangle.)

   My first step is ___ , because the problem asks for ___ .

   Show your work

You answered these out loud. Now write them.

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

1. 2

   Think it throughThe two known vertices of the park are 3 units apart, and each grid unit represents 100 feet. What is the park's width in feet?

   1. A3 feet
   2. B30 feet
   3. C103 feet
   4. D300 feet

   Why is that the answer?

   I chose ___ because ___ .
2. 3

   Think it throughThe park's area must be 240,000 sq ft and its width is 300 ft. What is its length?

   1. A720 feet
   2. B800 feet
   3. C80,000 feet
   4. D240,300 feet

   How do you know?

   I chose ___ because ___ .
3. 4

   Think it throughThe 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. A0.8 units
   2. B8 units
   3. C80 units
   4. D800 units

   Explain your thinking.

   I chose ___ because ___ .
4. 5

   Back to the modelThe vertices (-4.5, 3) and (5, 3) share y = 3, so the side between them is horizontal, with length |5 − (−4.5)| = 9.5. Why is that side's length found by comparing the x-coordinates instead of the y-coordinates?

   The side is horizontal because both vertices share the same ___-coordinate.

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• (2, 5) and (2, -3)
• (-4, 1) and (6, 1)
• (0, 0) and (4, 3)
• (-4.5, 3) and (5, 3)
• (1, 2) and (5, 7)
• (5, 3) and (5, -3.75)
• (-2, -2) and (3, 4)
• (7, -1) and (-3, -1)

Use the words

Fill each blank with a word from the bank.

• A corner point of a polygon, named by an ordered pair, is a ___.
• A closed figure made of line segments is a ___.
• The total distance around a polygon is its ___.
• When two vertices share a coordinate, subtract the other and take the ___ ___.

Explain the thinking

1. 6

   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: Subtracting coordinates without the absolute value — from y = 3 down to y = −3.
2. 7

   Say moreYou sorted pairs of vertices into 'subtract coordinates' versus 'slanted.' How did you decide that (0, 0) and (4, 3) belonged in the slanted group?

   (0, 0) and (4, 3) are slanted because they don't share the same ___ or the same ___.
3. 8

   Change one numberGo back to Part 1 and pick one problem you already solved. Change one number in it, then solve your new version. Show every step.

   If ___ changed to ___ , then ___ .

   Show your work

Last check

These two come from Lesson 7.6. If they are shaky, that is the lesson to revisit — not this one.

1. 9

   Show what you knowQuick check — you've got this: A rectangle has vertices (-1, 4), (5, 4), (5, 1), (-1, 1). What is its perimeter?

   1. A6 units
   2. B9 units
   3. C18 units
   4. D18 square units

   Explain your choice.

   I know it is ___ because ___ .
2. 10

   From Lesson 7.6Quick check — you've got this: What is the distance between the points (3, -2) and (3, 5)?

   1. A3 units
   2. B5 units
   3. C7 units
   4. D9 units
3. 11

   From Lesson 7.6What is the total flight path?

   1. A2 units
   2. B7 units
   3. C12 units
   4. D35 units

Be honest — this tells your teacher what to do next