6th Grade Math Worksheets - Free Printable

Let’s solve this step by step.

We are given a face drawn on a coordinate grid, and we need to find the coordinates of each labeled point (A through H) for Part 1. Then in Part 2, we draw our own face and list its outline points — but since that’s creative and not fixed, we’ll focus on Part 1 first, which has definite answers.

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Part 1: Write down the coordinates of each point of the face.

Remember: Coordinates are written as (x, y)
→ x is how far left or right from the center (horizontal axis)
→ y is how far up or down from the center (vertical axis)

Let’s go point by point:

- Point A: Look at the top-left ear tip. It’s at x = -3, y = 4 → (-3, 4)
- Point B: Bottom-left of left ear. x = -4, y = 2 → (-4, 2)
- Point C: Left eye (brown oval). Center looks like x = -2, y = 1 → (-2, 1)
- Point D: Right eye. Symmetric to C → x = 2, y = 1 → (2, 1)
- Point E: Nose (gray circle). At origin? Wait — it’s at x = 0, y = -1 → (0, -1)
- Point F: Mouth (smile curve bottom). Looks like x = 0, y = -3 → (0, -3)
- Point G: Bottom-right of chin? Actually, looking at the jawline — Point G is at x = 3, y = -2 → (3, -2)
- Point H: Top-right ear tip. Symmetric to A → x = 3, y = 4 → (3, 4)

Wait — let me double-check with the grid lines.

Looking again carefully:

The grid goes from -5 to 5 on both axes.

- A: Left ear top — definitely (-3, 4)
- B: Left ear bottom — (-4, 2) — yes
- C: Left eye — centered between x=-1 and x=-3? No — actually, the brown oval for left eye spans from x=-3 to x=-1, so center is x=-2, y=1 → correct
- D: Right eye — same height, x=2 → (2,1)
- E: Nose — gray circle at (0, -1) — yes
- F: Mouth — the lowest point of the smile is at (0, -3) — yes
- G: This is tricky. The label “G” is near the lower right side of the face outline. Looking at the polygonal outline of the face, after F (mouth), the line goes to G, then to H. From the drawing, G appears to be at (3, -2)
- H: Right ear top — (3, 4)

But wait — let’s check symmetry. The face is symmetric left-right.

So if A is (-3,4), H should be (3,4) → matches.

If B is (-4,2), then the corresponding point on the right should be (4,2)? But there’s no label for that. Instead, G is labeled at what looks like (3,-2). Let’s trace the outline:

Starting from top-left ear: A(-3,4) → down to B(-4,2) → then to... probably next point is near (-3,0)? But not labeled. Then to C(-2,1)? That doesn’t make sense because C is an eye, not on the outer edge.

Actually, re-examining: The labels A–H are placed on specific features, not necessarily all on the outer contour.

Looking at the diagram again (mentally):

- A: top of left ear → (-3,4)
- B: bottom of left ear → (-4,2)
- C: left eye → (-2,1)
- D: right eye → (2,1)
- E: nose → (0,-1)
- F: mouth → (0,-3)
- G: right side of jaw/chin area → likely (3,-2)
- H: top of right ear → (3,4)

Yes, that seems consistent.

Now, let’s write them in order as requested:

A ( __ , __ ) → (-3, 4)
B ( __ , __ ) → (-4, 2)
C ( __ , __ ) → (-2, 1)
D ( __ , __ ) → (2, 1)
E ( __ , __ ) → (0, -1)
F ( __ , __ ) → (0, -3)
G ( __ , __ ) → (3, -2)
H ( __ , __ ) → (3, 4)

Wait — is G really (3,-2)? Let me think about the shape.

From F (0,-3), the line goes to G, then to H (3,4). If G is (3,-2), that makes a straight line from (0,-3) to (3,-2) to (3,4)? That would mean from G to H is vertical — which matches the drawing: from jaw up to ear along x=3.

Similarly, on the left: from B(-4,2) to ... probably to some point, then to A(-3,4). But since only A and B are labeled on the left ear, and G and H on the right, it’s asymmetric labeling? Or maybe I misread.

Alternative interpretation: Maybe G is the point where the jaw meets the neck on the right? In many such diagrams, G might be (4, -2) or something.

Wait — let’s count grid squares.

Assume each square is 1 unit.

From origin (0,0):

- Move left 3, up 4 → A → (-3,4) ✔️
- Move left 4, up 2 → B → (-4,2) ✔️
- Left 2, up 1 → C → (-2,1) ✔️
- Right 2, up 1 → D → (2,1) ✔️
- Down 1 → E → (0,-1) ✔️
- Down 3 → F → (0,-3) ✔️
- Now G: from F(0,-3), moving right 3 and up 1 → (3,-2) → that seems right for the jaw corner.
- H: from G(3,-2) straight up to y=4 → (3,4) ✔️

Yes, that fits.

So final coordinates for Part 1:

A (-3, 4)
B (-4, 2)
C (-2, 1)
D (2, 1)
E (0, -1)
F (0, -3)
G (3, -2)
H (3, 4)

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Part 2: Draw your own face using the grid below and write down the coordinates of the outline.

This part is open-ended — you’re supposed to draw your own face and pick points around the outline. Since we can’t draw here, and the instruction says “write down the coordinates”, but without a specific figure, we can’t give exact answers. However, for the purpose of this response, since the user likely expects only Part 1 solved (as Part 2 is creative), and the problem says “solve the problem accurately”, we’ll provide Part 1 answers.

But note: The worksheet says “Draw your own face... and write down the coordinates”. So technically, any set of coordinates forming a face outline would be acceptable. But since no specific answer is expected for Part 2 (it’s student-created), we’ll focus on Part 1.

However, to be thorough, let’s assume they want us to recognize that Part 2 is variable, so we won’t invent arbitrary points unless asked.

But the main solvable part is Part 1.

Final verification:

Check symmetry:

Left side: A(-3,4), B(-4,2), C(-2,1)
Right side: H(3,4), G(3,-2)? Wait, G is not symmetric to B. B is (-4,2), symmetric would be (4,2), but G is (3,-2). That suggests G is not the mirror of B.

Perhaps G is meant to be the right-side equivalent of some other point.

Maybe I misidentified G.

Looking back: In the diagram, after F (mouth at 0,-3), the line goes to a point on the right jaw, labeled G, then up to H (ear top).

In standard such worksheets, often the points are:

- A: left ear top
- B: left ear bottom
- C: left eye
- D: right eye
- E: nose
- F: mouth
- G: right jaw bottom or chin right
- H: right ear top

And typically, the face outline might have points like:

Start at A(-3,4) → B(-4,2) → say P(-3,0) → Q(-1,-2) → F(0,-3) → R(1,-2) → S(3,0) → G(4,2) → H(3,4) — but that’s not matching labels.

Given the labels provided, and common practice, I think my initial assignment is correct.

Another way: Perhaps G is (4, -2)? Let's see.

If G were (4,-2), then from F(0,-3) to G(4,-2) is a line, then to H(3,4). But H is at (3,4), so from (4,-2) to (3,4) is possible, but less symmetric.

Whereas if G is (3,-2), then from F(0,-3) to G(3,-2) is slope (1/3), then G to H(3,4) is vertical — which matches the drawing where the right side of the face goes straight up from jaw to ear.

Similarly, on the left, from B(-4,2) to A(-3,4) is a line, and presumably from B down to some point, but not labeled.

I think (3,-2) for G is correct.

To confirm, let's list all:

A: (-3, 4)
B: (-4, 2)
C: (-2, 1)
D: (2, 1)
E: (0, -1)
F: (0, -3)
G: (3, -2)
H: (3, 4)

Yes.

For Part 2, since it's "draw your own", we can't provide a single answer, but if forced to give an example, we could say:

Example for Part 2 (not required, but for completeness):

Suppose you draw a simple oval face with points:

Outline points:
P1: (-2, 3)
P2: (-3, 0)
P3: (-2, -3)
P4: (0, -4)
P5: (2, -3)
P6: (3, 0)
P7: (2, 3)

But again, this is arbitrary.

Since the problem likely expects only Part 1 to be filled, and Part 2 is for the student to do, we'll provide Part 1 answers.

Final Answer:

Part 1:
A (-3, 4)
B (-4, 2)
C (-2, 1)
D (2, 1)
E (0, -1)
F (0, -3)
G (3, -2)
H (3, 4)

Part 2: [Student draws their own face and lists coordinates; no single correct answer]

But since the instruction is to solve the problem accurately, and Part 2 is subjective, we'll box only Part 1 as the definitive answer.

However, looking at the worksheet format, it has blanks for A-H in Part 1, and then for Part 2, it has A-G for the new face. So perhaps for Part 2, they expect the student to define their own points, but since we're solving, we should note that.

But to adhere to the task, I'll provide the Part 1 answers as the solution.

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Final Answer:
A (-3, 4)
B (-4, 2)
C (-2, 1)
D (2, 1)
E (0, -1)
F (0, -3)
G (3, -2)
H (3, 4)