Coordinate grid worksheet for students to practice finding and plotting points on a Cartesian plane.

Let’s solve this step by step.

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Part 1a: Find coordinates of points A, B, and C

We look at the grid:

- Point A is at x = 1, y = 6 → So A (1, 6)
- Point B is at x = 1, y = 3 → So B (1, 3)
- Point C is at x = 5, y = 3 → So C (5, 3)

✔ Checked: All points are correctly read from the grid.

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Part 1b & 1c: Plot point D to make a rectangle with A, B, C

We have:
- A (1,6)
- B (1,3)
- C (5,3)

Notice:
- A and B share same x (x=1), so vertical line.
- B and C share same y (y=3), so horizontal line.

To make a rectangle, we need a fourth point D that completes the shape.

From A (1,6), if we go right as far as from B to C (which is 4 units: 5 - 1 = 4), we get to x = 1 + 4 = 5.

From C (5,3), if we go up as far as from B to A (which is 3 units: 6 - 3 = 3), we get to y = 3 + 3 = 6.

So D should be at (5, 6)

Check:
- A(1,6) to D(5,6): horizontal
- D(5,6) to C(5,3): vertical
- C(5,3) to B(1,3): horizontal
- B(1,3) to A(1,6): vertical

Yes — all angles are right angles, opposite sides equal → Rectangle!

✔ So D is at (5, 6)

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Part 1d: Plot E(7,6), F(7,8), G(9,8), H(9,6)

These are given. We don’t plot them here since it’s text-based, but we note their positions for part 2.

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Part 2: Join E, F, G, H — what shape?

List the points:

- E (7,6)
- F (7,8)
- G (9,8)
- H (9,6)

Plotting mentally:

- E to F: vertical up (same x=7, y from 6 to 8)
- F to G: horizontal right (same y=8, x from 7 to 9)
- G to H: vertical down (same x=9, y from 8 to 6)
- H to E: horizontal left (same y=6, x from 9 to 7)

All sides are straight, adjacent sides perpendicular, opposite sides equal.

Also, check side lengths:

- Vertical sides: length = 8 - 6 = 2
- Horizontal sides: length = 9 - 7 = 2

Wait — all sides are length 2? Then it’s not just a rectangle — it’s a square!

But let’s confirm:

EF: |8 - 6| = 2
FG: |9 - 7| = 2
GH: |8 - 6| = 2
HE: |9 - 7| = 2

And angles are 90° because movements are only horizontal/vertical.

✔ So joining E-F-G-H forms a square.

But wait — sometimes in school math, they might accept “rectangle” too, since a square is a special rectangle. But since all sides are equal, the most precise answer is square.

However, looking back at the question: “see what shape will be formed?” — and given the context of the worksheet (coordinates, rectangles earlier), they may expect “rectangle”. But technically, it’s a square.

Let me double-check coordinates:

E(7,6), F(7,8), G(9,8), H(9,6)

Distance EF: √[(7-7)² + (8-6)²] = √[0 + 4] = 2
Distance FG: √[(9-7)² + (8-8)²] = √[4 + 0] = 2
Distance GH: √[(9-9)² + (6-8)²] = √[0 + 4] = 2
Distance HE: √[(7-9)² + (6-6)²] = √[4 + 0] = 2

All sides equal → Square.

Also, diagonals: EG from (7,6) to (9,8): √[(2)² + (2)²] = √8
FH from (7,8) to (9,6): √[(2)² + (-2)²] = 8 → equal diagonals, which confirms square.

✔ Final decision: It’s a square.

But let’s see what the worksheet expects. In many elementary/middle school contexts, if they haven’t introduced squares separately, they might say rectangle. However, since the problem says “what shape”, and it’s clearly a square, we should say square.

Alternatively, maybe they want “rectangle” because part 1 was about making a rectangle. But no — part 2 is separate.

Looking again: The points E,F,G,H form a quadrilateral with all sides equal and right angles → definitely a square.

I think it’s safe to say square.

But let me check one more thing: Is there any trick? No — coordinates are clear.

Final Answer:

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Final Answer:
1a. A (1, 6), B (1, 3), C (5, 3)
1c. D (5, 6)
2. Square