Start here

Use the model to solve the first problem. Then try these quick review questions from earlier lessons.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step. 🔊 Listen 💡 Hint

   Try it together — then prove it:

   1. 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.
   2. How many sides have each length? (Two sides of 9.5 and two sides of 6.75.)
   3. Find the perimeter. (2 × 9.5 + 2 × 6.75 = 19 + 13.5 = 32.5 units)
   4. Why is 9.5 × 6.75 not the perimeter? (9.5 × 6.75 is the area, the space inside. Perimeter is the distance around.)

   Show your work

Try these on your own

Choose an answer. Then explain how you know.

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? 🔊 Listen 💡 Hint

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

   Why is that the answer?
2. 3

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

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

   How do you know? Give a second reason as well.
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? 🔊 Listen 💡 Hint

   1. A0.8 units
   2. B8 units
   3. C80 units
   4. D800 units

   Explain your thinking. What would have to change for a different choice to be right?
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? 🔊 Listen 💡 Hint

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 mistakeRead the mistake. Explain what went wrong, then show the correct step. 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint
3. 8

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: A town-planning map shows a grid with two corner points of a future rectangular park already marked. The rest of the park is drawn only as a dashed outline waiting for its other two corners. 🔊 Listen 💡 Hint

   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 knowExplain your thinking — A rectangle has vertices (-1, 4), (5, 4), (5, 1), (-1, 1). What is its perimeter? 🔊 Listen 💡 Hint

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

   Explain your choice.
2. 10

   From Lesson 7.6Explain your thinking — What is the distance between the points (3, -2) and (3, 5)? 🔊 Listen 💡 Hint

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

   How do you know?
3. 11

   From Lesson 7.6What is the total flight path? 🔊 Listen 💡 Hint

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

   How do you know?

Check your progress

Choose the box that best describes how you feel about each skill.