Respan Dataset Explorer

Ally is excited to compete in a 
\[6\]-mile race. The race organizers plotted the course on a coordinate map. The starting point is at 
\[(4,3)\], and the ending point is at 
\[(4,9)\]. Ally's family decides to stand at 
\[(4,6)\] on the map.
Plot the starting point, ending point, and place where Ally's family stands on the map.
\[x\]
\[y\]
How far along will Ally be in the race when she reaches her family?
Choose 1 answer:
Choose 1 answer:
(Choice A)   Less than halfway through the race
A
Less than halfway through the race
(Choice B)   Halfway through the race
B
Halfway through the race
(Choice C)   More than halfway through the race
C
More than halfway through the race

To determine how far along Ally will be in the race when she reaches her family at point \((4, 6)\), we need to analyze the starting point \((4, 3)\) and the ending point \((4, 9)\) of the race.

1. **Calculate the total distance of the race**:  
   The race is \(6\) miles long.
   
2. **Determine the vertical distance from the starting point to where Ally's family stands**:
   - Starting point: \((4, 3)\)
   - Family's point: \((4, 6)\)

   The vertical distance from Ally's starting point to where her family is standing is:
   \[
   y_{family} - y_{start} = 6 - 3 = 3 \text{ miles}
   \]

3. **Calculate how far along the race Ally is when she reaches her family**:
   Since she is \(3\) miles into the race and the total distance of the race is \(6\) miles, we can find the fraction of the race completed:
   - Distance completed: \(3\) miles
   - Total distance: \(6\) miles

   To find out if this is less than, equal to, or more than halfway, we can compare \(3\) miles with half of \(6\) miles:
   \[
   \frac{6}{2} = 3
   \]

Since \(3\) miles is equal to \(3\) miles, when Ally reaches her family, she will be exactly halfway through the race.

### Conclusion:
The correct choice is **(Choice B) Halfway through the race**.

Use the following coordinate plane to write the ordered pair for each point.
A coordinate grid is labeled 0 through 6 on the x-axis and the y-axis. Three plot points are on different parts of the grid. Point A is 5 units up from the origin on the y-axis. Point B is 1 unit to the right and 3 units up from the origin. Point C is 4 units to the right and 3 units up from the origin.
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[C\]
\[B\]
\[A\]
\[y\]
\[x\]
Point	Ordered pair
\[\greenD{A}\]	
\[(\] 
 , 
 
\[)\]
\[\purpleC{B}\]	
\[(\] 
 , 
 
\[)\]
\[\blueD{C}\]	
\[(\] 
 , 
 
\[)\]

To write the ordered pairs for each point according to their descriptions on the coordinate grid, let's analyze each point given:

1. **Point A**: It is located 5 units up from the origin on the y-axis.
   - Since it is 5 units up and there is no horizontal movement (x-coordinate is 0), the ordered pair is:
   \[
   \text{Point A} \Rightarrow (0, 5)
   \]

2. **Point B**: It is located 1 unit to the right and 3 units up from the origin.
   - This means the x-coordinate is 1 (right) and the y-coordinate is 3 (up).
   \[
   \text{Point B} \Rightarrow (1, 3)
   \]

3. **Point C**: It is located 4 units to the right and 3 units up from the origin.
   - This means the x-coordinate is 4 (right) and the y-coordinate is 3 (up).
   \[
   \text{Point C} \Rightarrow (4, 3)
   \]

### Summary of Ordered Pairs:
- Point A: \((0, 5)\)
- Point B: \((1, 3)\)
- Point C: \((4, 3)\)

### Final Answers:
- **Point A**: \((0, 5)\)
- **Point B**: \((1, 3)\)
- **Point C**: \((4, 3)\)

What is the x-coordinate of the point plotted below?
A coordinate grid is labeled from 1 to 6 from the origin in both the x and y-axis. A blue point is 6 units up from the origin on the y-axis. 
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[y\]
\[x\]


2 of 5

The point plotted is described as being "6 units up from the origin on the y-axis." 

In coordinate terms, if a point is located on the y-axis, its x-coordinate is always 0 (since there is no horizontal movement from the origin). Therefore, if the point is 6 units up from the origin, the coordinates of that point would be \((0, 6)\).

The x-coordinate of this point is:

\[
\text{x-coordinate} = 0
\]

So, the answer is **0**.

What is the y-coordinate of the point plotted below?
A coordinate grid is labeled from 1 to 6 from the origin in both the x and y-axis. A blue point is 6 units to the right of and 1 unit up from the origin. 
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[y\]
\[x\]

The point is described as being "6 units to the right of and 1 unit up from the origin." 

In coordinate terms:
- Moving 6 units to the right from the origin gives an x-coordinate of \(6\).
- Moving 1 unit up from the origin gives a y-coordinate of \(1\).

Thus, the coordinates of the point are \((6, 1)\).

### The y-coordinate of the point is:
\[
1
\]

So the answer is **1**.

What is the y-coordinate of the point plotted below?
A coordinate grid is labeled from 1 to 6 from the origin in both the x and y-axis. A blue point is 6 units to the right of and 1 unit up from the origin. 
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[y\]
\[x\]

The point is described as being "6 units to the right of and 1 unit up from the origin."

- Moving **6 units to the right** means the x-coordinate is \(6\).
- Moving **1 unit up** means the y-coordinate is \(1\).

Therefore, the coordinates of the point are \((6, 1)\).

### The y-coordinate of the point is:
\[
1
\]

So the answer is **1**.

Which ordered pair is not graphed below?
A coordinate grid is labeled 0 through 6 on the x-axis and the y-axis. Three plot points are on different parts of the grid. From left to right the first plot point is at the origin. The second plot point is 3 units to the right from the origin on the x-axis. The last plot point is 3 units to the right and 3 units up from the origin.
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[y\]
\[x\]
Choose 1 answer:
Choose 1 answer:
(Choice A)   
\[(3,0)\]
A
\[(3,0)\]
(Choice B)   
\[(3,3)\]
B
\[(3,3)\]
(Choice C)   
\[(0,0)\]
C
\[(0,0)\]
(Choice D)   
\[(0,3)\]
D
\[(0,3)\]

Let's analyze the plotted points based on the descriptions provided and determine which ordered pair is not graphed.

1. **First plot point at the origin**: 
   - The coordinates are \((0, 0)\).

2. **Second plot point, 3 units to the right from the origin on the x-axis**: 
   - The coordinates are \((3, 0)\).

3. **Third plot point, 3 units to the right and 3 units up from the origin**: 
   - The coordinates are \((3, 3)\).

### Summary of the graphed points:

- \((0, 0)\): At the origin.
- \((3, 0)\): 3 units to the right on the x-axis.
- \((3, 3)\): 3 units to the right and 3 units up.

### Now, let's analyze each option:

- **(Choice A)**: \((3, 0)\) – This point is graphed (second plotted point).
  
- **(Choice B)**: \((3, 3)\) – This point is also graphed (third plotted point).
  
- **(Choice C)**: \((0, 0)\) – This point is graphed (first plotted point).
  
- **(Choice D)**: \((0, 3)\) – This point is **not** mentioned in the plotted points; thus, it is not graphed.

### Conclusion:
The ordered pair that is **not graphed** is **(Choice D) \((0, 3)\)**.

Plot the point 
\[(4,1)\].
\[x\]
\[y\]

To plot the point \((4, 1)\) on a coordinate grid, follow these steps:

1. **Locate the x-coordinate (4)**:
   - Move 4 units to the right along the x-axis from the origin (0,0).

2. **Locate the y-coordinate (1)**:
   - From the point where you reached x = 4, move 1 unit up along the y-axis.

The point \((4, 1)\) will be located at the intersection of the vertical line at \(x = 4\) and the horizontal line at \(y = 1\).

### Visualization:
- The x-axis runs horizontally and the y-axis runs vertically.
- Start at the origin (0,0).
- Move right to (4, 0).
- Then move up to reach (4, 1).

Once you follow these steps, you can mark the point \((4, 1)\) on your graph. If you have graph paper or a coordinate grid, simply place a dot or a point at that intersection and label it \((4, 1)\).

Plot the point 
\[(4,1)\].
\[x\]
\[y\]

To plot the point \((4, 1)\) on a coordinate grid, follow these steps:

1. **Draw the Coordinate Axes**:
   - Draw a vertical line for the y-axis and a horizontal line for the x-axis. They should intersect at the origin, which is the point \((0, 0)\).

2. **Label the Axes**:
   - Mark the x-axis with numbers (0, 1, 2, 3, 4, 5, etc.) and the y-axis with numbers (0, 1, 2, 3, 4, 5, etc.).

3. **Locate the x-coordinate**:
   - Since the x-coordinate of the point is \(4\), move \(4\) units to the right from the origin along the x-axis.

4. **Locate the y-coordinate**:
   - From the point \((4, 0)\) on the x-axis, move \(1\) unit up along the y-axis.

5. **Mark the Point**:
   - The intersection of the line you drew at \(x = 4\) and the line you drew at \(y = 1\) is the point \((4, 1)\).
   - You can place a dot or a point at this intersection and label it \((4, 1)\).

### Summary:
- The coordinates of the point is \((4, 1)\), which means \(4\) units along the x-axis and \(1\) unit along the y-axis.

If you can't visualize it, imagine the following:
- Starting from the origin (0, 0), move right to (4, 0), then move up to (4, 1). 

This is how to successfully plot the point \((4, 1)\) on the coordinate grid.

Ally is excited to compete in a 
\[6\]-mile race. The race organizers plotted the course on a coordinate map. The starting point is at 
\[(4,3)\], and the ending point is at 
\[(4,9)\]. Ally's family decides to stand at 
\[(4,6)\] on the map.
Plot the starting point, ending point, and place where Ally's family stands on the map.
\[x\]
\[y\]
How far along will Ally be in the race when she reaches her family?
Choose 1 answer:
Choose 1 answer:
(Choice A)   Less than halfway through the race
A
Less than halfway through the race
(Choice B)   Halfway through the race
B
Halfway through the race
(Choice C)   More than halfway through the race
C
More than halfway through the race
Related content
Report a problem

To determine how far along Ally will be in the race when she reaches her family at the point \((4, 6)\), we need to analyze the starting and ending points of the race.

### Starting and Ending Points
- **Starting Point**: \((4, 3)\)
- **Ending Point**: \((4, 9)\)

### Steps to Find the Distance to Ally's Family
1. **Calculate the total distance of the race**:
   The race is \(6\) miles long.

2. **Calculate the vertical distance from the starting point to where Ally's family is standing**:
   - Starting Point (y-coordinate): \(3\)
   - Family's Point (y-coordinate): \(6\)

   The vertical distance from Ally's starting point to where her family is standing is:
   \[
   y_{family} - y_{start} = 6 - 3 = 3 \text{ miles}
   \]

3. **Calculate how far along the race Ally is when she reaches her family**:
   When Ally reaches her family, she will have completed \(3\) miles of the \(6\) mile race.

### Analysis of the Race Completion
To compare Ally's progress with the total race distance:
- Total Race Distance: \(6\) miles
- Distance Completed: \(3\) miles

To determine whether this is less than, equal to, or more than halfway, we note:
\[
\frac{6}{2} = 3 \text{ miles}
\]

Since she has run exactly \(3\) miles, she is:
- **Exactly halfway through the race**.

### Conclusion
The correct choice is **(Choice B) Halfway through the race**.

Use the following coordinate plane to write the ordered pair for each point.
A coordinate grid is labeled 0 through 6 on the x-axis and the y-axis. Three plot points are on different parts of the grid. Point A is 2 units to the right and 2 unit up from the origin. Point B is 3 units to the right and 2 units up from the origin. Point C is 3 units to the right and 5 units up from the origin.
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[C\]
\[B\]
\[A\]
\[y\]
\[x\]
Point	Ordered pair
\[\greenD{A}\]	
\[(\] 
 , 
 
\[)\]
\[\purpleC{B}\]	
\[(\] 
 , 
 
\[)\]
\[\blueD{C}\]	
\[(\] 
 , 
 
\[)\]

To write the ordered pairs for each point based on the descriptions provided, let's analyze each point:

1. **Point A**: It is located 2 units to the right and 2 units up from the origin.
   - X-coordinate: \(2\) (2 units to the right)
   - Y-coordinate: \(2\) (2 units up)
   - **Ordered pair for Point A**: \((2, 2)\)

2. **Point B**: It is located 3 units to the right and 2 units up from the origin.
   - X-coordinate: \(3\) (3 units to the right)
   - Y-coordinate: \(2\) (2 units up)
   - **Ordered pair for Point B**: \((3, 2)\)

3. **Point C**: It is located 3 units to the right and 5 units up from the origin.
   - X-coordinate: \(3\) (3 units to the right)
   - Y-coordinate: \(5\) (5 units up)
   - **Ordered pair for Point C**: \((3, 5)\)

### Summary of Ordered Pairs:
- **Point A**: \((2, 2)\)
- **Point B**: \((3, 2)\)
- **Point C**: \((3, 5)\)

### Final Answers:
- **Point A**: \((2, 2)\)
- **Point B**: \((3, 2)\)
- **Point C**: \((3, 5)\)