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. Find the distance between (2, 3) and (2, 8).
   2. Which coordinate is the same? Which way does the line go? (x = 2, so the line goes up and down.)
   3. Find the distance. (8 − 3 = 5 units)
   4. Why do we subtract here, and not add? (Both points are on the same side of 0. The 3 units to (2, 3) are part of the 8 units to (2, 8).)

   Show your work
2. 2

   Quick reviewIn which quadrant is the point (-4, 5)? 🔊 Listen 💡 Hint

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

   How do you know?
3. 3

   Quick reviewWhich point is located on the x-axis? 🔊 Listen 💡 Hint

   1. A(-4, -4)
   2. B(0, 4)
   3. C(4, 4)
   4. D(4, 0)

   How do you know?
4. 4

   Quick reviewA point has a positive x-coordinate and a negative y-coordinate. Which quadrant is it in? 🔊 Listen 💡 Hint

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

   How do you know?

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughWhat is the horizontal distance from (−4, 0) to (3, 0)? 🔊 Listen 💡 Hint

   1. A1 unit
   2. B−1 unit
   3. C7 units
   4. D12 units

   Why is that the answer?
2. 6

   Think it throughWhat is the vertical distance from (3, 0) to (3, −5)? 🔊 Listen 💡 Hint

   1. A3 units
   2. B5 units
   3. C−5 units
   4. D8 units

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

   Think it throughWhat is the total flight path? 🔊 Listen 💡 Hint

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

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

   Back to the modelHow did you use coordinates and absolute value to find the distance between two points in the same row or column? 🔊 Listen 💡 Hint

Use the words

Fill each blank with a word from the bank.

• How far apart two points are on the coordinate plane is the ___.
• The distance of a number from zero, used to find distance between points, is its ___.
• The distance between two points along the x-direction is the ___.
• The distance between two points along the y-direction is the ___.

Explain the thinking

1. 9

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

   The mistake: A common mistake in Distance on the Coordinate Plane is subtracting the coordinates as if both points were on the same side of zero, instead of adding their absolute values when the points are on opposite sides.
2. 10

   Say moreOne point is at (-3, 1) and another is at (4, 1). How does absolute value help you find the distance across zero? 🔊 Listen 💡 Hint
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Tahira will walk from the middle school to the high school. The grid shows a map of the town, where each unit labeled on the grid represents one kilometer. 🔊 Listen 💡 Hint

   Show your work

Last check

These two come from Lesson 7.5. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain 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

   Explain your choice.
2. 13

   From Lesson 7.5Explain your thinking — Point P is located 6 units right and 3 units up from the origin. What ordered pair names point P? 🔊 Listen 💡 Hint

   1. A(0, 3)
   2. B(3, 6)
   3. C(6, 3)
   4. D(6, 0)

   How do you know?
3. 14

   From Lesson 7.5Which point is farthest to the right? 🔊 Listen 💡 Hint

   1. A(3, 6)
   2. B(0, 0)
   3. C(8, 2)
   4. DThey are all the same

   How do you know?

Check your progress

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