The Cartesian Art Halloween Jack-o-Lantern math worksheet page 2 ... - Free Printable

This is a Halloween Cartesian Art activity where you are asked to plot and connect points on a coordinate plane to create a Halloween-themed picture. The instructions say:

> *"Join each set of points in order using line segments."*

There are multiple sets of points, each starting with "Start" and ending with "Stop". You need to:

1. Plot each point on the coordinate grid.
2. Connect them in order with straight lines.
3. Each segment will form part of a larger image.

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🔍 Step-by-Step Solution

We'll go through each set of coordinates, interpret them, and describe what they likely draw. Since I can't draw directly here, I’ll guide you through plotting and explain the resulting shape.

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#### ✔ First Set:
Start (2, 15), (3, 14), (6, 14), (9, 12), (7, 12), (8, 10), (4, 12), (3, 10), (1, 12), (-2, 9), (-3, 12), (-7, 10), (-5, 13), (-10, 12), (-7, 14), (-6, 14), (-4, 15), (-1, 16) Stop

Let’s analyze this path:
- Starts at (2,15), moves right and down to (3,14), then across to (6,14).
- Then up/down to (9,12), back to (7,12), down to (8,10), left to (4,12), etc.
- It goes symmetrically to the left: (-3,12), (-7,10), (-5,13), (-10,12), (-7,14), (-6,14), (-4,15), (-1,16)

This forms a top part of a pumpkin or jack-o'-lantern, possibly the face outline or top of the head.

It's likely the top curve of a pumpkin with a slightly jagged edge.

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#### ✔ Second Set:
Start (-1, 16), (-3, 22), (0, 23), (2, 15), (3, 13), (2, 14), (1, 13), (0, 14), (+1, 13), (+1, 14), (+2, 14), (+1, 16) Stop

Wait — this seems like a typo or misordering. Let's check:
- Starts at (-1,16), goes to (-3,22) → that’s way up!
- Then (0,23), which is even higher.
- Then drops to (2,15), (3,13), (2,14), (1,13), (0,14), (1,13), (1,14), (2,14), (1,16)

Actually, let’s recheck the sequence:
> Start (-1, 16), (-3, 22), (0, 23), (2, 15), (3, 13), (2, 14), (1, 13), (0, 14), (+1, 13), (+1, 14), (+2, 14), (+1, 16) Stop

But note: (+1, 13) is same as (1,13), etc.

This looks like a stem or top of a pumpkin — it goes from (-1,16) up to (0,23), then curves down.

But wait: (-3,22) and (0,23) are very high — maybe it's the stem of the pumpkin?

But (0,23) is near the top of the graph. So this could be the stem of a pumpkin going up from the top.

Then it comes back down to (2,15), then zigzags to (1,16) — probably closing the stem.

So this might be the pumpkin stem.

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#### ✔ Third Set:
Start (5, 1), (7, 3), (4, 6), (5, 1) Stop

This is a small triangle: from (5,1) to (7,3) to (4,6) back to (5,1).

That’s a small triangle, possibly an eye or nose.

But (5,1) is low — near bottom. Maybe not.

Wait — this might be a triangle-shaped feature like a nose or mouth.

But more likely, this is one eye.

But only one? Wait — next set.

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#### ✔ Fourth Set:
Start (2, -4), (0, 1), (2, -4), (-2, -4) Stop

Wait: (2,-4), (0,1), (2,-4), (-2,-4)

This goes:
- (2,-4) → (0,1) → (2,-4) → (-2,-4)

But (2,-4) is repeated — so it draws a line from (2,-4) to (0,1), then back to (2,-4), then to (-2,-4).

That makes a V-shape or a chevron, but it’s odd.

Alternatively, perhaps it’s meant to be:
- (2,-4) → (0,1) → (-2,-4) → (2,-4)? But it says (2,-4), (-2,-4)

Wait — the sequence is: (2,-4), (0,1), (2,-4), (-2,-4)

So it draws:
- From (2,-4) to (0,1): upward diagonal
- Back to (2,-4): downward diagonal
- Then to (-2,-4): horizontal line left

So it's like a "V" with a horizontal tail? That doesn’t make sense.

Possibly a typo.

Wait — maybe it's meant to be:
> Start (2, -4), (0, 1), (-2, -4), (2, -4) Stop

But it says: (2,-4), (0,1), (2,-4), (-2,-4)

That would mean:
- (2,-4) → (0,1) → (2,-4) → (-2,-4)

So it draws a line up to (0,1), then back down to (2,-4), then left to (-2,-4).

That creates a "Y" shape? Or a triangle with extra leg.

Alternatively, maybe it's a mouth — but the mouth is usually lower.

Wait — (2,-4) and (-2,-4) are both at y = -4, so horizontal line.

(0,1) is high up — so this might be a triangle pointing up, but drawn incorrectly.

Wait — perhaps the intended shape is:
- (2,-4) → (0,1) → (-2,-4) → (2,-4)

But the given list is:
> Start (2, -4), (0, 1), (2, -4), (-2, -4) Stop

So it draws:
1. (2,-4) → (0,1)
2. (0,1) → (2,-4) ← back
3. (2,-4) → (-2,-4) ← left

So it draws two lines: one from (2,-4) to (0,1), back, then a horizontal line from (2,-4) to (-2,-4).

So the final shape is just a horizontal line from x=-2 to x=2 at y=-4, and a diagonal line from (2,-4) to (0,1).

Not closed.

Maybe it's a single eye? But it's not closed.

Wait — perhaps the next set continues.

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#### ✔ Fifth Set:
Start (2, -7), (4, -11), (6, -7), (8, -9), (11, -7), (9, -11), (6, -17), (3, -14), (0, -19), (4, -14), (6, -16), (9, -10), (10, -5), (7, -9), (6, -8), (5, -11), (3, -8), (0, -11), (2, -7) Stop

This is a long path.

Let’s trace it:

- (2,-7) → (4,-11): down-right
- → (6,-7): up-right
- → (8,-9): down-right
- → (11,-7): up-right
- → (9,-11): down-left
- → (6,-17): down-left
- → (3,-14): up-left
- → (0,-19): down-left
- → (4,-14): up-right
- → (6,-16): down-right
- → (9,-10): up-right
- → (10,-5): up-right
- → (7,-9): down-left
- → (6,-8): down-left
- → (5,-11): down-left
- → (3,-8): up-left
- → (0,-11): down-left
- → (2,-7): up-right

This is complex, but it starts and ends at (2,-7). It forms a large, irregular shape.

Looking at the points, this might be a ghost, bat, or pumpkin face.

But notice: it dips down to (0,-19) — very low.

Also, it has a loop around (6,-17), (3,-14), (0,-19), (4,-14), etc.

This could be the body of a ghost or a bat.

But let's look at the last set.

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#### ✔ Sixth Set:
Start (9, 12), (12, 8), (14, 3), (15, -2), (15, -8), (13, -14), (11, -17), (9, -20), (5, -22), (0, -22), (-4, -22), (-7, -21), (-9, -20), (-12, -18), (-14, -15), (-15, -12), (-16, -6), (-15, 1), (-14, 5), (-12, 9), (-10, 12), Stop

This is a long path starting at (9,12) and going down and left.

Let’s follow:

- (9,12) → (12,8): down-right
- → (14,3): down-right
- → (15,-2): down-right
- → (15,-8): down
- → (13,-14): down-left
- → (11,-17): down-left
- → (9,-20): down-left
- → (5,-22): down-left
- → (0,-22): left
- → (-4,-22): left
- → (-7,-21): up-right
- → (-9,-20): up-right
- → (-12,-18): up-right
- → (-14,-15): up-right
- → (-15,-12): up-right
- → (-16,-6): up-right
- → (-15,1): up-right
- → (-14,5): up-right
- → (-12,9): up-right
- → (-10,12): up-right

And stops.

Now, this path starts at (9,12) and goes down to (5,-22), then up along the left side to (-10,12).

So it forms a symmetrical shape — almost like a ghost or bat wing.

But it’s a continuous curve from right to left, dipping down and coming up.

Compare with earlier paths.

Wait — this path is very similar to the fifth set — both go down to y = -22.

But this one is longer and more symmetrical.

In fact, if you combine the fifth and sixth sets, you get a full pumpkin face or ghost.

But now I realize: this is a pumpkin with a stem.

Let me re-analyze.

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🎃 Final Interpretation: What Is the Picture?

After analyzing all the sets:

1. First set: Top of pumpkin (curved top) from (2,15) to (-1,16) — forming the top rim.
2. Second set: Stem — goes from (-1,16) up to (0,23), then down to (1,16) — forming a stem.
3. Third set: (5,1), (7,3), (4,6), (5,1) — a small triangle — likely a nose or eye.
4. Fourth set: (2,-4), (0,1), (2,-4), (-2,-4) — messy, but possibly a mouth?
- Wait — (0,1) is high — not likely.
5. Fifth set: Complex path from (2,-7) to (2,-7) — likely the face features.
6. Sixth set: Long path from (9,12) to (-10,12) — likely the outline of the pumpkin body.

Wait — actually, the sixth set starts at (9,12) and goes down to (5,-22), then up to (-10,12). That’s half a pumpkin?

But the first set is the top, and the sixth set is the bottom half?

Wait — no.

Let’s look at y-values:

- First set: y = 12 to 16 — top
- Second set: y = 16 to 23 — stem
- Fifth set: y = -7 to -22 — bottom
- Sixth set: y = 12 to -22 — full side

Ah! The sixth set is the main body of the pumpkin — it goes from (9,12) down to (5,-22), then up to (-10,12). So it’s a U-shaped curve forming the side of the pumpkin.

But the first set is the top, and the sixth set is the lower half?

Wait — the first set goes from (2,15) to (-1,16), but the sixth set starts at (9,12) — so not connected.

Wait — perhaps the sixth set is the right side, and there’s a left side?

But no — the sixth set goes from (9,12) to (-10,12), so it spans from x=9 to x=-10, and y=12 to y=-22.

So it’s a large U-shape — likely the main body of the pumpkin.

The first set is the top curve of the pumpkin.

But the first set ends at (-1,16), and the sixth set starts at (9,12) — not connected.

Wait — perhaps the sixth set is the entire outer contour.

Let’s see: it starts at (9,12), goes down to (5,-22), then up to (-10,12).

But (-10,12) is far left.

So this is a smooth curve from right to left, forming the outer shell of a pumpkin.

Then the first set is the top rim — but it’s separate.

Wait — maybe the first set is the top of the pumpkin, and the sixth set is the side, but they should meet.

But (9,12) vs (2,15) — not close.

Wait — perhaps I made a mistake.

Let’s look at the first set again:

- (2,15), (3,14), (6,14), (9,12), (7,12), (8,10), (4,12), (3,10), (1,12), (-2,9), (-3,12), (-7,10), (-5,13), (-10,12), (-7,14), (-6,14), (-4,15), (-1,16)

So it goes from (2,15) to (9,12), then back to (7,12), etc., then to (-10,12), then to (-1,16).

So it forms a curve from (2,15) to (-1,16), passing through (9,12) and (-10,12).

So it’s a wide arc — the top of the pumpkin.

Then the sixth set starts at (9,12) — same point!

So the first set ends at (-1,16), and the sixth set starts at (9,12) — but (9,12) is also in the first set.

So they share the point (9,12).

Similarly, the sixth set ends at (-10,12), and the first set has (-10,12) — so they connect.

Wait — the first set includes (9,12) and (-10,12), and the sixth set starts at (9,12) and ends at (-10,12).

So the first set is the top curve, and the sixth set is the side curve — but they both use (9,12) and (-10,12).

But the first set goes from (2,15) to (-1,16) via (9,12) and (-10,12), while the sixth set goes from (9,12) down to (5,-22), then up to (-10,12).

So the first set is the top, and the sixth set is the side, but they overlap at (9,12) and (-10,12).

But the sixth set is much longer — it goes down to y=-22.

So the complete pumpkin is formed by:
- The top arc from (2,15) to (-1,16) — first set
- The stem — second set
- The body — sixth set (from (9,12) down to (5,-22), then up to (-10,12))
- But the body is only one side?

Wait — the sixth set goes from (9,12) to (-10,12), so it covers the entire width.

But the first set is the top, and the sixth set is the side, but they overlap.

Perhaps the first set is the top, and the sixth set is the main body, but they are not connected.

Wait — the first set ends at (-1,16), and the sixth set starts at (9,12) — not the same.

But (9,12) is in the first set — so when you finish the first set, you're at (-1,16), then you start the second set at (-1,16).

So the second set is the stem, starting from (-1,16).

Then the third set is (5,1), (7,3), (4,6), (5,1) — a small triangle — likely a nose.

Then the fourth set: (2,-4), (0,1), (2,-4), (-2,-4) — still confusing.

But the fifth set is large — from (2,-7) to (2,-7) — likely the mouth.

And the sixth set is the main body.

But the sixth set starts at (9,12), which is in the first set — so if you plot both, you have:

- First set: top arc from (2,15) to (-1,16) via (9,12), (-10,12)
- Then second set: stem from (-1,16) up to (0,23), down to (1,16)
- Then third set: nose at (5,1)
- Then fourth set: something at (2,-4)
- Then fifth set: mouth from (2,-7) to (2,-7)
- Then sixth set: body from (9,12) down to (5,-22), up to (-10,12)

But (9,12) is already used — so the sixth set continues from the first set.

But the first set ends at (-1,16), so you can't go to (9,12) unless you jump.

Ah! Here's the key: each "Start" is independent.

So you do:

1. Draw the first set: (2,15) to (-1,16) — top of pumpkin
2. Start new: (-1,16) to (0,23) — stem
3. Start new: (5,1) to (5,1) — nose
4. Start new: (2,-4) to (-2,-4) — mouth?
5. Start new: (2,-7) to (2,-7) — another feature
6. Start new: (9,12) to (-10,12) — body

But (9,12) is already in the first set — so the body is drawn separately.

But the body starts at (9,12), which is on the top, so it should be connected.

So the complete pumpkin is:

- Top arc: first set — from (2,15) to (-1,16)
- Stem: second set — from (-1,16) to (0,23), back to (1,16)
- Body: sixth set — from (9,12) down to (5,-22), then up to (-10,12)
- But (9,12) and (-10,12) are also in the first set — so the body is attached.

But the first set is the top, and the sixth set is the side, but they don't connect.

Wait — the sixth set starts at (9,12), which is on the top, so it's the right side of the pumpkin.

Similarly, it ends at (-10,12), which is on the left.

So the sixth set is the entire side of the pumpkin, from right to left.

The first set is the top rim.

So when you draw both, you get a pumpkin with:
- A rounded top (first set)
- A stem (second set)
- A side profile (sixth set)
- And facial features (third, fourth, fifth sets)

But the sixth set is the main body — it's a U-shape from (9,12) to (-10,12) via (5,-22).

So the pumpkin is symmetric, with a bumpy top and a round body.

The facial features are likely:
- Nose: third set — (5,1), (7,3), (4,6), (5,1) — a small triangle
- Mouth: fifth set — from (2,-7) to (2,-7) — a complex path
- Eyes: fourth set — (2,-4), (0,1), (2,-4), (-2,-4) — likely a pair of eyes

But (0,1) is high — not for eyes.

Wait — perhaps the eyes are the third set and another.

But only one triangle.

Wait — maybe the third set is one eye, and the fourth set is the other.

But the fourth set is messy.

Perhaps the fifth set is the mouth.

Given the complexity, the most likely picture is a jack-o'-lantern with:
- Top rim (first set)
- Stem (second set)
- Body (sixth set)
- Facial features (third, fourth, fifth sets)

But to solve the problem, you need to:

✔ How to Solve:

1. Take a blank coordinate grid.
2. Plot each point in order.
3. Connect them with line segments.
4. Repeat for each "Start...Stop" group.
5. The final image should be a pumpkin with a stem and face.

🎉 Final Answer:

When you plot and connect all the points as instructed, you will reveal a Halloween pumpkin (jack-o'-lantern) with:
- A stem on top,
- A round body,
- And facial features like eyes, nose, and mouth.

This is a fun way to practice plotting coordinates and connecting them to create art.

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✔ To complete the task:
- Use graph paper or a digital tool.
- Plot each point in order.
- Connect them with straight lines.
- Do not skip any sets.
- The final image will be a pumpkin face.

Happy Halloween! 🎃