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Which of the following is the distance between the two points shown?

A graph with the x-axis starting at negative 4, with tick marks every one-half unit up to 4. The y-axis starts at negative 4, with tick marks every one-half unit up to 4. A point is plotted at negative 3.5, 0 and at 1.5, 0.

5 units
−5 units
2 units
−2 units
Question 2(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)

What is the distance from (−6, 8) to (−6, −12)?

−20 units
20 units
−4 units
4 units
Question 3(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane LC)

What is the distance between the two points plotted?

A graph with the x-axis starting at negative 10, with tick marks every one unit up to 10. The y-axis starts at negative 10, with tick marks every one unit up to 10. A point is plotted at 3, 5 and at 3, negative 6.

1 unit
11 units
−11 units
−1 unit
Question 4(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)

Which of the points plotted is farther away from (−7, 8), and what is the distance?

A graph with the x-axis starting at negative 10, with tick marks every one unit up to 10. The y-axis starts at negative 10, with tick marks every one unit up to 10. A point is plotted at negative 7, negative 5, at negative 7, 8 and at 5, 8.

Point (5, 8), and it is 11 units away
Point (5, 8), and it is 13 units away
Point (−7, −5), and it is 12 units away
Point (−7, −5), and it is 13 units away
Question 5(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)

Which of the points plotted is closer to (−6, 8), and what is the distance?

A graph with the x-axis starting at negative 10, with tick marks every one unit up to 10. The y-axis starts at negative 10, with tick marks every one unit up to 10. A point is plotted at negative 6, negative 5, at negative 6, 8 and at 5, 8.

Point (−6, −5), and it is 11 units away
Point (−6, −5), and it is 13 units away
Point (5, 8), and it is 11 units away
Point (5, 8), and it is 13 units away
Question 6(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)

A student starts a walk at (−6, 10). If the student walks 4 miles north, south, east, or west, which of the following could be their location at the end of the walk?

(10, −6), (6, −6), (−2, 14), (−10, 14)
(4, 10), (−14, 10), (−6, −2), (−6, 6)
(−6, 4), (−6, 6), (−2, 10), (4, 10)
(−10, 10), (−2, 10), (−6, 14), (−6, 6)
Question 7(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane LC)

What is the distance between the two points plotted?

A graph with the x-axis starting at negative 10, with tick marks every one unit up to 10. The y-axis starts at negative 10, with tick marks every one unit up to 10. A point is plotted at negative 7, negative 5 and at 3, negative 5.

4 units
10 units
−4 units
−10 units

1 answer

Let's solve each question step by step.

Question 1

To find the distance between the points (-3.5, 0) and (1.5, 0), use the distance formula in the x-axis because the y-coordinates are the same.

Distance \( = |x_1 - x_2| \)

So,

\[ Distance = |-3.5 - 1.5| = |-5| = 5 \text{ units} \]

Answer: 5 units

Question 2

To find the distance between the points (-6, 8) and (-6, -12), again the x-coordinates are the same, so we only need to consider the y-coordinates.

\[ Distance = |y_1 - y_2| = |8 - (-12)| = |8 + 12| = |20| = 20 \text{ units} \]

Answer: 20 units

Question 3

For the points (3, 5) and (3, -6), use the distance formula. Since the x-coordinates are the same, we focus only on the y-coordinates:

\[ Distance = |y_1 - y_2| = |5 - (-6)| = |5 + 6| = |11| = 11 \text{ units} \]

Answer: 11 units

Question 4

Find the distance from (-7, 8) to both points: (-7, -5) and (5, 8).

  1. For (-7, -5): \[ Distance = |-7 - (-7)| + |8 - (-5)| = 0 + |8 + 5| = |13| = 13 \text{ units} \]

  2. For (5, 8): \[ Distance = |-7 - 5| + |8 - 8| = |-12| + 0 = 12 \text{ units} \]

The farther point is (-7, -5) which is 13 units away.

Answer: Point (−7, −5), and it is 13 units away

Question 5

For the points (-6, -5) and (5, 8):

  1. From (-6, 8) to (-6, -5): \[ Distance = |-6 - (-6)| + |8 - (-5)| = 0 + |8 + 5| = |13| = 13 \text{ units} \]

  2. From (-6, 8) to (5, 8): \[ Distance = |-6 - 5| + |8 - 8| = |-11| + 0 = 11 \text{ units} \]

The closer point is (5, 8) which is 11 units away.

Answer: Point (5, 8), and it is 11 units away

Question 6

The student is at (-6, 10).

  • If they walk 4 miles north, south, east or west, they could end up at:
    • North: (-6, 10 + 4) = (-6, 14)
    • South: (-6, 10 - 4) = (-6, 6)
    • East: (-6 + 4, 10) = (-2, 10)
    • West: (-6 - 4, 10) = (-10, 10)

Thus, valid answers include (-6, 14) and (-6, 6).

Answer: (−6, 6), because it is one of the possible locations.

Question 7

For the points (-7, -5) and (3, -5): Since the y-coordinates are the same, we use the x-coordinates:

\[ Distance = |-7 - 3| = |-10| = 10 \text{ units} \]

Answer: 10 units

Final Answers Summary:

  1. 5 units
  2. 20 units
  3. 11 units
  4. Point (−7, −5), and it is 13 units away
  5. Point (5, 8), and it is 11 units away
  6. (−6, 6)
  7. 10 units