Graphing Christmas Coordinates Math Art Activity - Our Family Code - Free Printable

Let's solve this step-by-step to reveal the Christmas image by plotting the given coordinate pairs on the graph.

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Step 1: Understand the Task

We are given a list of coordinate pairs. Each pair represents two points on a Cartesian grid. We need to:
- Plot each pair of points.
- Connect them with straight lines.
- The resulting shape will form a Christmas-themed image.

The coordinates are grouped into three columns:

#### Left Column (Tree Base and Left Side):
1. (14, 0) → (16, 0)
2. (16, 0) → (16, 3)
3. (16, 3) → (25, 3)
4. (14, 0) → (14, 3)
5. (14, 3) → (5, 3)

#### Middle Column (Tree Middle and Right Side):
6. (5, 3) → (9, 10)
7. (9, 10) → (6, 10)
8. (6, 10) → (10, 17)
9. (10, 17) → (8, 17)
10. (8, 17) → (15, 30)

#### Right Column (Tree Right Side and Top):
11. (25, 3) → (21, 10)
12. (21, 10) → (24, 10)
13. (24, 10) → (20, 17)
14. (20, 17) → (22, 17)
15. (22, 17) → (15, 30)

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Step 2: Analyze the Coordinates

Let’s interpret what these lines create.

#### Left Side (Base and Left Trunk/Outline):
- From (14,0) to (16,0): horizontal line at bottom.
- (16,0) to (16,3): vertical line up — left edge of base.
- (16,3) to (25,3): horizontal line across — top of base.
- (14,0) to (14,3): vertical line up — right edge of base? Wait, no — actually this is the *left* side.
- So from (14,0) to (14,3): vertical line on the left.
- (14,3) to (5,3): horizontal line leftward — completing the base rectangle?

Wait — that seems odd. Let's re-express.

Actually, the first five lines seem to form a rectangle from x=5 to x=25, y=0 to y=3?

But let's check:

- (14,0) to (16,0): bottom middle
- (16,0) to (16,3): up
- (16,3) to (25,3): right
- (14,0) to (14,3): up on left
- (14,3) to (5,3): left

Wait — that suggests:
- Bottom: from (5,3) to (25,3) via (14,3) and (16,3)? Not directly connected.
But we have:
- (14,3) → (5,3): leftward
- (16,3) → (25,3): rightward
So together, they form a horizontal line from (5,3) to (25,3), but not directly connected.

But (14,3) to (5,3) and (16,3) to (25,3) are both drawn.

So the base is a rectangle from (5,3) to (25,3), but only the top edge is drawn in two parts.

And the bottom edge is from (14,0) to (16,0).

Wait — maybe it's a trapezoid or tree trunk?

Let’s plot the key points:

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Plotting Key Points

Let’s go through each line:

#### Lines 1–5: Tree Base (Trunk?)
1. (14,0) to (16,0): horizontal line at bottom center
2. (16,0) to (16,3): vertical up
3. (16,3) to (25,3): horizontal right
4. (14,0) to (14,3): vertical up
5. (14,3) to (5,3): horizontal left

So now we have:
- A rectangle from x=5 to x=25, y=3 to y=3? No — wait, only the top of the base is drawn from (5,3) to (25,3).
- But the bottom is only from (14,0) to (16,0), which is narrow.

So the base is:
- Bottom: (14,0) to (16,0)
- Sides: (16,0) to (16,3), (14,0) to (14,3)
- Top: (14,3) to (5,3) and (16,3) to (25,3)

Wait — that means the top is wider than the bottom.

So it's like a trapezoid, wider at the top (from x=5 to x=25 at y=3), narrower at the bottom (x=14 to x=16 at y=0).

But (14,3) to (5,3) is leftward, and (16,3) to (25,3) is rightward — so yes, the top spans from x=5 to x=25 at y=3.

Bottom is from x=14 to x=16 at y=0.

So the trunk is a trapezoid, wide at the top, narrow at the bottom — unusual, but possible.

But then the tree branches start from y=3 upward.

Now look at the middle column:

#### Middle Column: Left Side of Tree
6. (5,3) → (9,10): diagonal up-right
7. (9,10) → (6,10): left horizontal
8. (6,10) → (10,17): diagonal up-right
9. (10,17) → (8,17): left horizontal
10. (8,17) → (15,30): diagonal up-right

This looks like a zigzagging path going up the left side of the tree.

Similarly, the right column:

11. (25,3) → (21,10): diagonal down-left
12. (21,10) → (24,10): right horizontal
13. (24,10) → (20,17): diagonal down-left
14. (20,17) → (22,17): right horizontal
15. (22,17) → (15,30): diagonal down-left

This is symmetric to the left side, but mirrored.

Let’s analyze:

- Left side: (5,3) → (9,10) → (6,10) → (10,17) → (8,17) → (15,30)
- Right side: (25,3) → (21,10) → (24,10) → (20,17) → (22,17) → (15,30)

Notice that both sides converge at (15,30) — the top of the tree!

Also, observe symmetry:
- Left: starts at (5,3), goes to (15,30)
- Right: starts at (25,3), goes to (15,30)

And the zigzag pattern suggests layers of the tree.

Let’s try to see the overall structure.

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Reconstructing the Image

Let’s sketch mentally:

1. Base:
- Bottom: (14,0) to (16,0)
- Left side: (14,0) to (14,3)
- Right side: (16,0) to (16,3)
- Top: (14,3) to (5,3) and (16,3) to (25,3)
- So the base is a wide rectangle from x=5 to x=25 at y=3, but only 2 units wide at bottom (x=14–16). That doesn't make sense unless it's a trunk.

Wait — perhaps the base is meant to be a rectangular platform?

But (14,3) to (5,3) is left, and (16,3) to (25,3) is right — so the top edge of the base is from (5,3) to (25,3), and the bottom is from (14,0) to (16,0).

So the base is a trapezoid:
- Bottom: x=14 to 16 at y=0
- Top: x=5 to 25 at y=3

So it’s wider at the top than bottom — like a flared trunk.

Then the tree grows from there.

Now, from (5,3), the left side goes:
- (5,3) → (9,10): up-right
- (9,10) → (6,10): left
- (6,10) → (10,17): up-right
- (10,17) → (8,17): left
- (8,17) → (15,30): up-right

Similarly, right side:
- (25,3) → (21,10): down-left? Wait — (25,3) to (21,10): x decreases, y increases → up-left
- (21,10) → (24,10): right
- (24,10) → (20,17): up-left
- (20,17) → (22,17): right
- (22,17) → (15,30): up-left

So both sides go toward the center (15,30).

Now notice:
- At y=10: left has (9,10) and (6,10); right has (21,10) and (24,10)
- At y=17: left has (10,17) and (8,17); right has (20,17) and (22,17)

So the tree has three layers:
1. Bottom layer: from y=3 to y=10
2. Middle layer: y=10 to y=17
3. Top layer: y=17 to y=30

Each layer is made of two horizontal lines (left and right) and diagonals connecting them.

Let’s reconstruct:

#### Layer 1 (y=3 to y=10):
- Left: (5,3) → (9,10)
- Then horizontal: (9,10) → (6,10) — wait, that’s leftward!
- Then (6,10) → (10,17) — up to next layer

Wait — that suggests the left side is not continuous.

But if you connect:
- (5,3) → (9,10)
- (9,10) → (6,10): back to left
- (6,10) → (10,17)

So it's forming a zigzag.

Similarly on the right:
- (25,3) → (21,10)
- (21,10) → (24,10): right
- (24,10) → (20,17)

So the pattern is:
- Start at (5,3), go up-right to (9,10)
- Then go left to (6,10)
- Then go up-right to (10,17)
- Then go left to (8,17)
- Then go up-right to (15,30)

Similarly on right:
- (25,3) → (21,10)
- (21,10) → (24,10)
- (24,10) → (20,17)
- (20,17) → (22,17)
- (22,17) → (15,30)

So the left side of the tree is:
- (5,3) → (9,10) → (6,10) → (10,17) → (8,17) → (15,30)

But this is not smooth — it zigzags.

But if we connect all the points in order, we get a zigzagging outline for the left side of the tree.

Similarly for the right.

Now, notice that:
- The top of the tree is at (15,30)
- The base is from (5,3) to (25,3) at y=3
- The tree is symmetric around x=15

So the entire figure is a Christmas tree with:
- A flared base (wider at top of trunk)
- Three triangular sections (layers)
- Zigzag edges to suggest branches

But wait — the lines are drawn as separate segments.

Let’s think about the final shape.

When you draw:
- Left side: (5,3) → (9,10) → (6,10) → (10,17) → (8,17) → (15,30)
- Right side: (25,3) → (21,10) → (24,10) → (20,17) → (22,17) → (15,30)

And the base: from (5,3) to (25,3) at y=3, but only via (14,3) and (16,3)

Wait — but (5,3) to (14,3) is not directly connected? No — we have (14,3) to (5,3), so yes, it is.

So the top of the trunk is a horizontal line from (5,3) to (25,3)

Then the tree starts from (5,3) and (25,3) and goes up to (15,30)

But the path is zigzagging.

However, when you connect all the lines, the outline forms a triangular Christmas tree with zigzag edges to represent branches.

Moreover, notice that:
- The left side goes: (5,3) → (9,10) → (6,10) → (10,17) → (8,17) → (15,30)
- This creates a sawtooth pattern on the left

Similarly on the right.

But since the tree is symmetric, and both sides meet at (15,30), the final image is a Christmas tree with:
- A trunk from y=0 to y=3, narrow at bottom, wide at top
- A tree above, with zigzag edges

But the trunk is only 2 units wide at bottom (14–16), but 20 units wide at top (5–25), so it's inverted — wider at top.

That’s unusual — typically trees are wider at bottom.

But maybe it’s a stylized tree.

Alternatively, perhaps the base is meant to be the ground, and the trunk is just the area from (14,0) to (16,0) and up.

Wait — let’s reconsider.

Maybe the base is just the small rectangle from (14,0) to (16,3), and the top of the trunk is from (5,3) to (25,3), but that would mean the trunk expands outward — which is odd.

But perhaps the entire base is from (5,3) to (25,3), and the ground is only shown from (14,0) to (16,0) — but that doesn’t make sense.

Wait — look again:

- (14,0) to (16,0): ground line
- (16,0) to (16,3): up
- (16,3) to (25,3): right
- (14,0) to (14,3): up
- (14,3) to (5,3): left

So the trunk is a rectangle from (5,3) to (25,3) at top, but only from (14,0) to (16,0) at bottom.

So it’s like a narrow base supporting a wide trunk — perhaps it’s a stump or platform.

But then the tree grows from the top of the trunk.

So the tree starts at y=3, from x=5 to x=25.

Then the tree outline goes up from (5,3) to (15,30) and from (25,3) to (15,30), with zigzag edges.

Thus, the final image is a Christmas tree with:
- A trunk that is wide at the top (5 to 25 at y=3), narrow at the bottom (14 to 16 at y=0)
- A tree with zigzag branches

But that’s not realistic.

Wait — perhaps the trunk is just the area from (14,0) to (16,3), and the platform from (5,3) to (25,3) is not part of the trunk, but rather the ground level?

No — because (14,3) to (5,3) is drawn, so it's part of the same structure.

Alternatively, maybe the entire base is a rectangle from x=5 to x=25, y=0 to y=3, but only the corners are connected.

But we don't have (5,0) or (25,0).

We only have:
- (14,0) to (16,0)
- (14,0) to (14,3)
- (16,0) to (16,3)
- (14,3) to (5,3)
- (16,3) to (25,3)

So the only connections are:
- Bottom: (14,0) to (16,0)
- Left: (14,0) to (14,3)
- Right: (16,0) to (16,3)
- Top: (14,3) to (5,3) and (16,3) to (25,3)

So the top edge is from (5,3) to (25,3), but only via (14,3) — so it's not continuous.

But since both (14,3) to (5,3) and (16,3) to (25,3) are drawn, and (14,3) and (16,3) are connected vertically, the top is fully connected from (5,3) to (25,3).

Similarly, the bottom is only from (14,0) to (16,0).

So the base is a trapezoid:
- Bottom: (14,0) to (16,0)
- Top: (5,3) to (25,3)
- Left: (14,0) to (14,3) and (14,3) to (5,3)
- Right: (16,0) to (16,3) and (16,3) to (25,3)

Wait — no: (14,3) to (5,3) is leftward, and (16,3) to (25,3) is rightward.

So the top is from (5,3) to (25,3), and the bottom is from (14,0) to (16,0).

So the base is a trapezoid with:
- Bottom: 2 units wide (x=14 to 16)
- Top: 20 units wide (x=5 to 25)
- Height: 3 units

So it's wider at the top — like an inverted cone.

Then the tree grows from the top edge of this trapezoid.

From (5,3) and (25,3), the tree goes up to (15,30), with zigzag edges.

So the tree is a large triangle with zigzag borders.

Thus, the final image is a Christmas tree with:
- A flared base (trapezoidal, wider at top)
- A triangular tree above, with zigzag branches

But the zigzag might represent ornaments or branch patterns.

Alternatively, the zigzag is just the outline of the tree.

But when you connect the points in order, the left side is:
- (5,3) → (9,10) → (6,10) → (10,17) → (8,17) → (15,30)

This is not a smooth curve — it’s a series of V-shapes.

Similarly on the right.

So the tree has two layers of zigzags.

Let’s count the segments:

- From (5,3) to (9,10): up-right
- (9,10) to (6,10): left
- (6,10) to (10,17): up-right
- (10,17) to (8,17): left
- (8,17) to (15,30): up-right

So it’s like a zigzag with two "teeth".

Similarly on the right.

So the tree has two sets of branches.

And the top is at (15,30), the star or top ornament.

Therefore, the revealed image is a Christmas tree with:
- A wide base (trapezoidal)
- Zigzag branches
- A star at the top

But the base is wider at the top, which is odd.

Alternatively, perhaps the base is just the ground, and the tree starts at (5,3) to (25,3), and the trunk is only the narrow part.

But the drawing includes (14,0) to (16,0), so it's likely the trunk.

Given the symmetry and the convergence at (15,30), the most likely answer is that the image is a Christmas tree.

To confirm, let’s consider the final shape:

- The tree is symmetric around x=15
- It starts at y=3, from x=5 to x=25
- Goes up to (15,30)
- With zigzag edges
- Base is a trapezoid from (14,0) to (16,0) up to (5,3) to (25,3)

So the full image is a Christmas tree with a wide trunk and zigzag branches.

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✔ Final Answer:

The plotted lines form a Christmas tree with:
- A trapezoidal base (wider at the top, narrower at the bottom)
- Zigzagging branches on both sides
- A star or top ornament at (15,30)

This is a stylized representation of a Christmas tree, where the zigzag lines represent the branches or decorations.

You can complete the image by:
1. Plotting each point on the grid.
2. Connecting the points in order.
3. Observing the symmetric, tree-like shape.

The completed image should resemble a Christmas tree with a wide base and a pointed top.

🎉 Merry Christmas!