📍 Coordinates — Grade 5

Learn to read, plot and move points on a coordinate grid — including all four quadrants!

1. The Coordinate Grid

A coordinate grid has two axes:

The x-axis goes left and right (horizontal)
The y-axis goes up and down (vertical)
They cross at the origin, which is (0, 0)

We write coordinates as (x, y) — the x-value first, then the y-value.

Quadrant 1

(+, +)
Top right

Quadrant 2

(−, +)
Top left

Quadrant 3

(−, −)
Bottom left

Quadrant 4

(+, −)
Bottom right

2. Plotting Points

Remember: "Along the corridor, up the stairs"

Move along the x-axis first (left/right)
Then move up or down the y-axis

To plot (3, 5): go 3 right, then 5 up.

To plot (−2, 4): go 2 left, then 4 up.

3. Negative Coordinates

Numbers to the left of the y-axis are negative x-values.

Numbers below the x-axis are negative y-values.

(−3, −2) is in Quadrant 3 — 3 left and 2 down from the origin.

4. Shapes on a Grid — Midpoints

To find the midpoint of two points, add the x-values and divide by 2, then add the y-values and divide by 2.

Midpoint of (2, 4) and (6, 8):

x: (2 + 6) ÷ 2 = 4

y: (4 + 8) ÷ 2 = 6

Midpoint = (4, 6)

5. Translations

A translation slides a shape without rotating or flipping it.

A translation vector (a, b) means: move a in the x-direction and b in the y-direction.

Translate (3, 2) by vector (4, −1):

New x = 3 + 4 = 7

New y = 2 + (−1) = 1

New point = (7, 1)

Translate by (3, −2) means: right 3, down 2.

📍 Worked Examples

Example 1 — Reading Coordinates

A point P is at (4, −3). What is its y-coordinate?

The y-coordinate is the second value: −3

Example 2 — Distance

Points A = (1, 2) and B = (6, 2). How far apart are they?

Same y-value, so it's a horizontal distance: 6 − 1 = 5 units

Example 3 — Midpoint

Find the midpoint of (−4, 2) and (2, 6).

x: (−4 + 2) ÷ 2 = −1

y: (2 + 6) ÷ 2 = 4

Midpoint = (−1, 4)

Example 4 — Translation

Translate (−2, 3) by vector (5, −4).

New x = −2 + 5 = 3

New y = 3 + (−4) = −1

New point = (3, −1)

Example 5 — Missing Vertex

Three corners of a rectangle are (1,1), (5,1), (5,4). Find the fourth corner.

The missing corner must have x=1 (same as first point) and y=4 (same as third point).

Fourth corner = (1, 4)

🔭 Coordinate Plotter

Plot Points (up to 5)

P1 x

P1 y

P2 x

P2 y

P3 x

P3 y

P4 x

P4 y

P5 x

P5 y

Midpoint Calculator

x1

y1

x2

y2

Exercise 1 — Reading Coordinates

Use the points: A(3,5), B(−2,4), C(−4,−3), D(1,−5), E(0,3), F(5,0), G(−1,2), H(2,−2), I(−3,0), J(4,4)

1. What is the x-coordinate of A(3,5)?
2. What is the y-coordinate of B(−2,4)?
3. What is the x-coordinate of C(−4,−3)?
4. What is the y-coordinate of D(1,−5)?
5. What is the x-coordinate of E(0,3)?
6. What is the y-coordinate of F(5,0)?
7. What is the x-coordinate of G(−1,2)?
8. What is the y-coordinate of H(2,−2)?
9. What is the x-coordinate of I(−3,0)?
10. What is the y-coordinate of J(4,4)?

Exercise 2 — Distances and Midpoints

Find horizontal or vertical distances, and midpoints.

1. Distance from (1,3) to (6,3) — horizontal distance? units
2. Distance from (2,1) to (2,8) — vertical distance? units
3. Midpoint of (0,0) and (4,6) — enter the x-coordinate.
4. Midpoint of (0,0) and (4,6) — enter the y-coordinate.
5. Distance from (−3,2) to (4,2) — horizontal distance? units
6. Distance from (1,−4) to (1,3) — vertical distance? units
7. Midpoint of (2,4) and (8,4) — enter the x-coordinate.
8. Midpoint of (2,4) and (8,4) — enter the y-coordinate.
9. Midpoint of (−2,−4) and (4,2) — enter the x-coordinate.
10. Midpoint of (−2,−4) and (4,2) — enter the y-coordinate.

Exercise 3 — Negative Coordinates

1. Point (−5, 3) — enter the x-coordinate.
2. Point (2, −7) — enter the y-coordinate.
3. Point (−4, −4) — enter the x-coordinate.
4. Which quadrant is (−3, 2) in? (1/2/3/4)
5. Which quadrant is (4, −5) in? (1/2/3/4)
6. Which quadrant is (−2, −6) in? (1/2/3/4)
7. Point (−1, 5): enter the y-coordinate.
8. Point (3, −4): enter the x-coordinate.
9. Which quadrant is (5, 3) in? (1/2/3/4)
10. Point (0, −3): enter the y-coordinate.

Exercise 4 — Translations

Apply the translation vector to find the new coordinate asked.

1. Translate (2, 3) by (4, 1). Enter new x.
2. Translate (2, 3) by (4, 1). Enter new y.
3. Translate (−1, 4) by (3, −2). Enter new x.
4. Translate (−1, 4) by (3, −2). Enter new y.
5. Translate (5, −2) by (−3, 4). Enter new x.
6. Translate (5, −2) by (−3, 4). Enter new y.
7. Translate (0, 0) by (−4, −5). Enter new x.
8. Translate (0, 0) by (−4, −5). Enter new y.
9. Translate (−3, −1) by (6, 3). Enter new x.
10. Translate (−3, −1) by (6, 3). Enter new y.

Exercise 5 — Missing Vertex of Shapes

Find the missing corner of each rectangle or square. Enter x or y as asked.

1. Rectangle corners: (1,1),(5,1),(5,4). Missing corner x = ?
2. Rectangle corners: (1,1),(5,1),(5,4). Missing corner y = ?
3. Rectangle corners: (0,0),(4,0),(4,3). Missing corner x = ?
4. Rectangle corners: (0,0),(4,0),(4,3). Missing corner y = ?
5. Rectangle corners: (−2,1),(3,1),(3,5). Missing corner x = ?
6. Rectangle corners: (−2,1),(3,1),(3,5). Missing corner y = ?
7. Square corners: (0,0),(4,0),(4,4). Missing corner x = ?
8. Square corners: (0,0),(4,0),(4,4). Missing corner y = ?
9. Rectangle corners: (−3,−2),(2,−2),(2,1). Missing corner x = ?
10. Rectangle corners: (−3,−2),(2,−2),(2,1). Missing corner y = ?

Practice — 20 Questions

1. Point (4,7): enter the x-coordinate.
2. Point (−3,5): enter the y-coordinate.
3. Distance from (2,3) to (9,3). units
4. Translate (1,2) by (3,4). New x = ?
5. Which quadrant is (−4,−1)? (1/2/3/4)
6. Midpoint of (0,0) and (6,4): enter x.
7. Midpoint of (0,0) and (6,4): enter y.
8. Translate (3,−1) by (−2,5). New y = ?
9. Rectangle corners (0,0),(5,0),(5,3). Missing corner x = ?
10. Rectangle corners (0,0),(5,0),(5,3). Missing corner y = ?
11. Point (−6,2): enter the x-coordinate.
12. Distance from (1,−3) to (1,4). units
13. Translate (−2,−3) by (5,1). New x = ?
14. Which quadrant is (3,−2)?
15. Midpoint of (−4,2) and (2,8): enter x.
16. Midpoint of (−4,2) and (2,8): enter y.
17. Translate (0,5) by (−3,−8). New y = ?
18. Point (7,−4): enter the y-coordinate.
19. Which quadrant is (−1,6)?
20. Distance from (−3,2) to (5,2). units

Challenge — 8 Hard Questions

1. Point A is at (−5,3). It is translated to (2,−1). What is the x component of the translation vector?
2. Point A is at (−5,3). It is translated to (2,−1). What is the y component of the translation vector?
3. Three corners of a square are (1,1),(4,1),(4,4). What is the x-coordinate of the fourth corner?
4. Three corners of a square are (1,1),(4,1),(4,4). What is the y-coordinate of the fourth corner?
5. Midpoint of AB is (3,2). A = (1,−2). What is the x-coordinate of B?
6. Midpoint of AB is (3,2). A = (1,−2). What is the y-coordinate of B?
7. A shape is reflected in the y-axis. A vertex was at (4,−3). What is its new x-coordinate?
8. A shape is reflected in the x-axis. A vertex was at (2,5). What is its new y-coordinate?