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 find the distance from (2, 3) to (2, 8). What do these points share? The same x = 2, so it is a vertical line. These points are on the SAME side of zero (both positive), so do we add or subtract? We subtract. The distance is |8 - 3| = 5 units. When points sit on the same side of zero, subtract to find the distance. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartIn which quadrant is the point (-4, 5)?

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

   How do you know?
3. 3

   Warm restartWhich point is located on the x-axis?

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

   How do you know?
4. 4

   Warm restartA point has a positive x-coordinate and a negative y-coordinate. Which quadrant is it in?

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

   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 throughWhat is the horizontal distance from (−4, 0) to (3, 0)?

   1. A7 units
   2. B1 unit
   3. C−1 unit
   4. D12 units

   Why is that the answer?
2. 6

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

   1. A5 units
   2. B−5 units
   3. C3 units
   4. D8 units

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

   Think it throughWhat is the total flight path?

   1. A12 units
   2. B2 units
   3. C35 units
   4. D7 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?

Use the words

Fill each blank with a word from the bank.

• When two points share a coordinate, the distance is the ___ ___ of the difference.
• 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 ___.

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 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?
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.

   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)?

   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?

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

   How do you know?
3. 14

   From Lesson 7.5Which point is farthest to the right?

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

   How do you know?

Be honest — this tells your teacher what to do next