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

   Let's do one together:

   1. Find the distance between (2, 3) and (2, 8).
   2. Which coordinate is the same? (x = 2, so the line goes up and down.)
   3. Are 3 and 8 on the same side of 0? (Yes. Both are positive.)
   4. Do we add or subtract? Find the distance. (Subtract: 8 − 3 = 5)

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

   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
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)
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

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?

   I chose ___ because ___ .
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?

   I chose ___ because ___ .
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.

   I chose ___ because ___ .
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

   The points ___ and ___ share the same ___ -coordinate. To find the distance, I found |___| + |___| = ___, which equals ___ units.

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

   The distance is |4| + |-3|, which equals ___.
3. 11

   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. 🔊 Listen 💡 Hint

   If ___ changed to ___ , then ___ .

   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 knowQuick check — you've got this: 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.

   I know it is ___ because ___ .
2. 13

   From Lesson 7.5Quick check — you've got this: 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)
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

Check your progress

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