Question
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 6, 4 and at 5, 4.
1 unit
−1 unit
11 units
−11 units
Question 2(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)
Which of the points plotted is closer to (−4, 5), 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 4, negative 5, at negative 4, 5 and at 5, 5.
Point (−4, −5), and it is 9 units away
Point (−4, −5), and it is 10 units away
Point (5, 5), and it is 9 units away
Point (5, 5), and it is 10 units away
Question 3(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)
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, 0 and at 0.5, 0.
2.5 units
3.5 units
−3.5 units
−2.5 units
Question 4(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 6, 4 and at negative 6, negative 6.
2 units
−2 units
10 units
−10 units
Question 5(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 6(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)
Which of the points plotted is farther away from (4, 4), 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, 4, at 4, 4 and at 4, negative 5.
Point (4, −5), and it is 9 units away
Point (4, −5), and it is 11 units away
Point (−7, 4), and it is 9 units away
Point (−7, 4), and it is 11 units away
Question 7(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)
What is the distance from (−3, 10) to (−3, −9)?
−1 unit
−19 units
1 unit
19 units
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 6, 4 and at 5, 4.
1 unit
−1 unit
11 units
−11 units
Question 2(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)
Which of the points plotted is closer to (−4, 5), 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 4, negative 5, at negative 4, 5 and at 5, 5.
Point (−4, −5), and it is 9 units away
Point (−4, −5), and it is 10 units away
Point (5, 5), and it is 9 units away
Point (5, 5), and it is 10 units away
Question 3(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)
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, 0 and at 0.5, 0.
2.5 units
3.5 units
−3.5 units
−2.5 units
Question 4(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 6, 4 and at negative 6, negative 6.
2 units
−2 units
10 units
−10 units
Question 5(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 6(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)
Which of the points plotted is farther away from (4, 4), 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, 4, at 4, 4 and at 4, negative 5.
Point (4, −5), and it is 9 units away
Point (4, −5), and it is 11 units away
Point (−7, 4), and it is 9 units away
Point (−7, 4), and it is 11 units away
Question 7(Multiple Choice Worth 2 points)
(Distance on the Coordinate Plane MC)
What is the distance from (−3, 10) to (−3, −9)?
−1 unit
−19 units
1 unit
19 units
Answers
GPT-4o mini
Let's solve each question step-by-step:
**Question 1:**
What is the distance between the two points (-6, 4) and (5, 4)?
To calculate the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substituting the coordinates:
\[
d = \sqrt{(5 - (-6))^2 + (4 - 4)^2} = \sqrt{(5 + 6)^2 + (0)^2} = \sqrt{11^2} = 11 \text{ units}
\]
So the answer is: **11 units**.
---
**Question 2:**
Which of the points plotted is closer to (−4, 5)?
- For (−4, -5):
\[
d = \sqrt{(-4 - (-4))^2 + (5 - (-5))^2} = \sqrt{(0)^2 + (10)^2} = 10 \text{ units}
\]
- For (5, 5):
\[
d = \sqrt{(5 - (-4))^2 + (5 - 5)^2} = \sqrt{(9)^2 + (0)^2} = 9 \text{ units}
\]
The point (5, 5) is closer to (−4, 5), and the distance is **9 units**.
So the answer is: **Point (5, 5), and it is 9 units away**.
---
**Question 3:**
Which of the following is the distance between the two points (-3, 0) and (0.5, 0)?
Using the distance formula:
\[
d = \sqrt{(0.5 - (-3))^2 + (0 - 0)^2} = \sqrt{(0.5 + 3)^2} = \sqrt{(3.5)^2} = 3.5 \text{ units}
\]
So the answer is: **3.5 units**.
---
**Question 4:**
What is the distance between the two points (-6, 4) and (-6, -6)?
Using the distance formula:
\[
d = \sqrt{(-6 - (-6))^2 + (-6 - 4)^2} = \sqrt{(0)^2 + (-10)^2} = \sqrt{100} = 10 \text{ units}
\]
So the answer is: **10 units**.
---
**Question 5:**
If the student starts at (−6, 10) and walks 4 miles:
- If they walk north: (−6, 14)
- If they walk south: (−6, 6)
- If they walk east: (-2, 10)
- If they walk west: (-10, 10)
The options that could be their location at the end of the walk are:
- **(−6, 14)**, **(−6, 6)**, **(−2, 10)**, **(−10, 10)** (but we need to choose a set that is valid).
The correct choice among given options is: **(−6, 6), (−2, 10), (4, 10)** which corresponds to valid movements.
So the answer is: **(−6, 6)**.
---
**Question 6:**
Which of the points plotted is farther away from (4, 4)?
- For (−7, 4):
\[
d = \sqrt{(-7 - 4)^2 + (4 - 4)^2} = \sqrt{(-11)^2} = 11 \text{ units}
\]
- For (4, -5):
\[
d = \sqrt{(4 - 4)^2 + (-5 - 4)^2} = \sqrt{(0)^2 + (-9)^2} = 9 \text{ units}
\]
The point (−7, 4) is farther at **11 units**.
So the answer is: **Point (−7, 4), and it is 11 units away**.
---
**Question 7:**
What is the distance from (−3, 10) to (−3, −9)?
Using the distance formula:
\[
d = \sqrt{(-3 - (-3))^2 + (-9 - 10)^2} = \sqrt{(0)^2 + (-19)^2} = \sqrt{361} = 19 \text{ units}
\]
So the answer is: **19 units**.
**Question 1:**
What is the distance between the two points (-6, 4) and (5, 4)?
To calculate the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substituting the coordinates:
\[
d = \sqrt{(5 - (-6))^2 + (4 - 4)^2} = \sqrt{(5 + 6)^2 + (0)^2} = \sqrt{11^2} = 11 \text{ units}
\]
So the answer is: **11 units**.
---
**Question 2:**
Which of the points plotted is closer to (−4, 5)?
- For (−4, -5):
\[
d = \sqrt{(-4 - (-4))^2 + (5 - (-5))^2} = \sqrt{(0)^2 + (10)^2} = 10 \text{ units}
\]
- For (5, 5):
\[
d = \sqrt{(5 - (-4))^2 + (5 - 5)^2} = \sqrt{(9)^2 + (0)^2} = 9 \text{ units}
\]
The point (5, 5) is closer to (−4, 5), and the distance is **9 units**.
So the answer is: **Point (5, 5), and it is 9 units away**.
---
**Question 3:**
Which of the following is the distance between the two points (-3, 0) and (0.5, 0)?
Using the distance formula:
\[
d = \sqrt{(0.5 - (-3))^2 + (0 - 0)^2} = \sqrt{(0.5 + 3)^2} = \sqrt{(3.5)^2} = 3.5 \text{ units}
\]
So the answer is: **3.5 units**.
---
**Question 4:**
What is the distance between the two points (-6, 4) and (-6, -6)?
Using the distance formula:
\[
d = \sqrt{(-6 - (-6))^2 + (-6 - 4)^2} = \sqrt{(0)^2 + (-10)^2} = \sqrt{100} = 10 \text{ units}
\]
So the answer is: **10 units**.
---
**Question 5:**
If the student starts at (−6, 10) and walks 4 miles:
- If they walk north: (−6, 14)
- If they walk south: (−6, 6)
- If they walk east: (-2, 10)
- If they walk west: (-10, 10)
The options that could be their location at the end of the walk are:
- **(−6, 14)**, **(−6, 6)**, **(−2, 10)**, **(−10, 10)** (but we need to choose a set that is valid).
The correct choice among given options is: **(−6, 6), (−2, 10), (4, 10)** which corresponds to valid movements.
So the answer is: **(−6, 6)**.
---
**Question 6:**
Which of the points plotted is farther away from (4, 4)?
- For (−7, 4):
\[
d = \sqrt{(-7 - 4)^2 + (4 - 4)^2} = \sqrt{(-11)^2} = 11 \text{ units}
\]
- For (4, -5):
\[
d = \sqrt{(4 - 4)^2 + (-5 - 4)^2} = \sqrt{(0)^2 + (-9)^2} = 9 \text{ units}
\]
The point (−7, 4) is farther at **11 units**.
So the answer is: **Point (−7, 4), and it is 11 units away**.
---
**Question 7:**
What is the distance from (−3, 10) to (−3, −9)?
Using the distance formula:
\[
d = \sqrt{(-3 - (-3))^2 + (-9 - 10)^2} = \sqrt{(0)^2 + (-19)^2} = \sqrt{361} = 19 \text{ units}
\]
So the answer is: **19 units**.