Year 6 Maths: Negative Coordinates

Introduction to Negative Coordinates

Hello Year 6! Today, we are going to learn about negative coordinates. This is an important topic in maths, especially when we work with graphs and maps. Don’t worry; I will explain it step by step!

What are Coordinates?

Coordinates are a way to find a point on a grid. We use two numbers to show a point’s position. These numbers are called x-coordinates and y-coordinates.

• The first number (x-coordinate) tells us how far to move left or right.
• The second number (y-coordinate) tells us how far to move up or down.

What are Negative Coordinates?

Negative coordinates are simply points that are to the left of the origin or below the origin on a graph.

• Origin: This is the point (0, 0) where the x-axis and y-axis cross.
• Negative x-coordinates: These are numbers like -1, -2, -3, etc. They mean you move left from the origin.
• Negative y-coordinates: These are numbers like -1, -2, -3, etc. They mean you move down from the origin.

Visualising Negative Coordinates

Imagine a piece of graph paper:

• If you start at (0, 0) and move left to (-1, 0), you are at the negative x-coordinate.
• If you move down to (0, -1), you are at the negative y-coordinate.

Here’s a little chart to help you:

      y      |      |  -2  |  (0,2)  -1  |   -----|---------- x      |     0  |        |     1  |     2  |   

Key Rules

1. Negative x-coordinates: Always move to the left from (0, 0).
2. Negative y-coordinates: Always move down from (0, 0).
3. Coordinates are written in brackets like this: (x, y).

Tips and Tricks

• Remember that moving left means you’re using negative numbers for x-coordinates.
• Moving down means you’re using negative numbers for y-coordinates.
• Use a graph to practice plotting points with negative coordinates!

Questions

Easy Level Questions

1. What is the coordinate of the point two units left and one unit up from the origin?
2. Plot the point (-3, 0) on a graph.
3. If a point is at (0, -2), how many units down is it from the origin?
4. What does (-1, -1) mean in terms of movement on a graph?
5. Which direction do you move to get to (-2, 3)?
6. How many units left do you go to reach (-4, 0)?
7. If you move from (0, 0) to (0, -3), which coordinate is negative?
8. What is the x-coordinate of (2, -2)?
9. Plot the point (0, -1) on a graph.
10. If you move to (-5, -2), are both coordinates negative?
11. If you start at (0, 0) and move left 1 unit, what is your new coordinate?
12. What is the coordinate of the point 3 units down from (0, 0)?
13. Is the point (-6, 4) in the negative x or y region?
14. What does the point (0, 0) represent?
15. If you move right and down, which coordinates will be positive?
16. How many units left do you go to reach (-1, 2)?
17. What coordinate is at (-3, -3)?
18. If you are at (0, 0) and move down 4 units, what is your coordinate?
19. What is the y-coordinate of the point (-2, 0)?
20. If you are at (-4, 1), are you in the negative or positive x region?

Medium Level Questions

1. If you plot the point (-2, -3), where will it be located on the graph?
2. How far is the point (-5, 0) from the origin?
3. Plot the points (3, -4) and (-1, -2) on a graph.
4. What is the distance from the origin to (-3, -2)?
5. Which quadrant does the point (-4, 3) belong?
6. If you move to (-2, -3) from the origin, how many units do you move down?
7. What is the coordinate of a point 3 units left and 2 units down from the origin?
8. If a point is at (0, -5), how many units down is it from the origin?
9. What is the x-coordinate for the point (-3, 4)?
10. If you are at (-1, 0) and move down 3 units, what is your new coordinate?
11. Where will you be if you start at (0, 0) and move left 5 units and down 2 units?
12. What is the y-coordinate of the point (-6, -1)?
13. If you travel to (-2, 2), how far are you from the y-axis?
14. What is the coordinate of a point 4 units down and 4 units left from the origin?
15. If the point is (-4, -4), what does that mean in terms of movement?
16. How many units right do you need to go from (-5, 0) to reach (0, 0)?
17. If you start at (0, 0) and move down 4 units and then left 2 units, what is your new coordinate?
18. What quadrant does the point (-3, -5) belong to?
19. How can you describe the point (0, -4)?
20. If you are at (0, 0) and go left 3 units and down 1 unit, where do you land?

Hard Level Questions

1. Calculate the distance between the points (-3, -4) and (0, 0).
2. If you have the point (-2, y) and you know y = -5, what is the point?
3. What is the midpoint between the points (-4, -2) and (0, 0)?
4. If you plot the points (-1, -2) and (2, 1), what type of triangle do they form with the origin?
5. If a point is represented as (-x, -y), what happens when you make both x and y positive?
6. What is the area of a rectangle formed by the coordinates (-2, -3), (0, -3), (0, 0), and (-2, 0)?
7. How do you determine if a point (-x, -y) lies in the third quadrant?
8. If you have the coordinates (-3, -2), what is the corresponding reflection in the first quadrant?
9. If you move from (0, 0) to (-5, -5), what is the total distance moved?
10. What is the equation of the line that passes through (0, -3) and (-2, -3)?
11. If the coordinates are (-4, y) and you know the distance from the origin is 5, what could y be?
12. How can you use negative coordinates to find the perimeter of a triangle with vertices at (0, 0), (-3, -3), and (-3, 0)?
13. What does the point (-5, 3) mean in terms of movement on a graph?
14. If you have a line segment from (-1, -1) to (1, 1), what are the coordinates of its midpoint?
15. How can you represent the coordinates (-3, -4) in a real-world context?
16. If you move left from (-2, 0) to (-5, 0), how far did you move?
17. What is the slope of the line that connects the points (-1, -1) and (-5, -5)?
18. If you reflect the point (-2, -3) over the x-axis, what are the new coordinates?
19. How do you find the distance between the points (-3, -4) and (-3, 0)?
20. If you start at (0, 0) and move to (-2, -6), in which direction did you move?

Answers

Easy Level Answers

1. (-2, 1)
2. Left two units on the x-axis.
3. 2 units down.
4. Move left and down from the origin.
5. Left 2, up 3.
6. 4 units left.
7. y-coordinate is negative.
9. Down 1 unit.
10. Yes, both are negative.
11. (-1, 0)
12. (0, -4)
13. Negative x-region.
14. Origin point.
15. Right (positive x) and down (negative y).
16. 1 unit left.
17. Negative x.
18. (0, -4)
19. -2.
20. In the negative x-region.

Medium Level Answers

1. Left two, down three.
2. 5 units.
3. Plot (3, -4) and (-1, -2).
4. 3.61 units.
5. Second quadrant.
6. Down three units.
7. (-3, -2).
8. 5 units down.
9. -3.
10. (-1, -3).
11. (-5, -2).
12. -6.
13. 2 units.
14. (-4, -4).
15. Negative x and y.
16. 5 units.
17. (-2, -4).
18. Third quadrant.
19. (-2, 2).
20. (-3, -1).

Hard Level Answers

1. 5 units.
2. (-2, -5).
3. (-2, -1).
4. A right-angled triangle.
5. Moves to the first quadrant.
6. 6 square units.
7. Both coordinates are negative.
8. (2, 3).
9. Total distance is 7.07 units.
10. y = -3.
11. y could be 4 or -4.
12. 6 units.
13. Left 5, up 3.
14. (0, -1).
15. A point on the graph.
16. 3 units.
18. (-2, 3).
19. 4 units.
20. (-2, -6).

I hope this helps you understand negative coordinates better! Keep practicing, and you’ll get the hang of it in no time!