Coordinate Plane Worksheets - 15 Worksheets Library - Free Printable

Let’s solve this step by step.

We are given a coordinate grid with points labeled A through H. We need to:

1. Write the ordered pair (x, y) for each point.
2. Answer 5 questions about distances and quadrants.

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Step 1: Find coordinates of each point

Remember:
- The first number is the x-coordinate (left/right).
- The second number is the y-coordinate (up/down).
- Start at origin (0,0). Move right/left for x, up/down for y.

Let’s go point by point:

- Point A: Go left 4, up 3 → (-4, 3)
- Point B: Go left 3, up 6 → (-3, 6)
- Point C: Go right 3, up 1 → (3, 1)
- Point D: Go right 3, up 6 → (3, 6)
- Point E: Go left 4, down 5 → (-4, -5)
- Point F: Go right 5, up 4 → (5, 4)
- Point G: Go right 3, down 3 → (3, -3)
- Point H: Go left 2, down 2 → (-2, -2)

So we have:

A(-4, 3)
B(-3, 6)
C(3, 1)
D(3, 6)
E(-4, -5)
F(5, 4)
G(3, -3)
H(-2, -2)

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Step 2: Answer the questions

Question 1: Distance between point D and G

D = (3, 6), G = (3, -3)

Same x-coordinate → vertical line.

Distance = difference in y-values: |6 - (-3)| = |6 + 3| = 9

✔ Answer: 9

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Question 2: Quadrant of point H

H = (-2, -2)

Negative x, negative y → that’s Quadrant III.

✔ Answer: III

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Question 3: Distance between point B and E

B = (-3, 6), E = (-4, -5)

Different x and y → use distance formula? But since it’s a grid, maybe count squares? Or use Pythagoras?

Actually, let’s do it properly.

Horizontal distance: |-3 - (-4)| = |1| = 1
Vertical distance: |6 - (-5)| = |11| = 11

Then distance = √(1² + 11²) = √(1 + 121) = √122 ≈ 11.05 — but wait, maybe they want exact or just counting?

Wait — looking at the graph, perhaps they expect us to count units along grid lines? But no, distance between two points not aligned horizontally/vertically should be straight-line distance.

But let me check if there’s a simpler way — maybe the problem expects Manhattan distance? No, usually in coordinate geometry, “distance” means Euclidean unless specified.

But let’s look again — maybe I made a mistake.

Wait — actually, in many middle school worksheets, if points are not aligned, they might still expect you to use the distance formula. But √122 is messy.

Alternatively — did I misread the points?

B is (-3,6), E is (-4,-5)

Δx = 1, Δy = 11 → yes.

But let me double-check the coordinates from the image description.

From earlier:

B: left 3, up 6 → (-3,6) ✔️
E: left 4, down 5 → (-4,-5) ✔️

So distance = √[(−3 − (−4))² + (6 − (−5))²] = √[1² + 11²] = √122

But √122 doesn’t simplify. Maybe they want it as is? Or perhaps I made an error.

Wait — maybe the question is asking for horizontal + vertical? Like city block distance? That would be 1 + 11 = 12.

But standard math curriculum uses Euclidean distance.

However, looking at Question 1 — D and G were vertical, so easy. For B and E, perhaps they expect the actual straight-line distance.

But let me see if there’s another interpretation.

Alternatively — maybe I misidentified point E?

Looking back: “E(-4, -5)” — yes, from the grid: x=-4, y=-5.

Perhaps the worksheet expects students to count the grid steps diagonally? Unlikely.

Wait — let me calculate numerically: √122 ≈ 11.045 — not nice.

Maybe I swapped points? No.

Another thought: Perhaps “distance” here means how many units apart along axes? But that’s not standard.

Wait — let me check online or recall: In some 6th grade materials, they might only ask for horizontal/vertical distances, but here B and E are not aligned.

But looking at the other questions — Q4 and Q5 are simple, Q1 was vertical.

Perhaps for Q3, they want the straight-line distance, and we leave it as √122? But that seems advanced.

Wait — let me re-express:

Maybe I can compute it as:

From B(-3,6) to E(-4,-5):

Move 1 unit left, 11 units down → so displacement vector ( -1, -11 )

Magnitude = √(1 + 121) = √122

I think we have to go with that.

But let me see if the answer is expected to be integer — probably not.

Alternatively — did I misread point E?

In the original problem, point E is at (-4, -5)? Let me confirm from the initial analysis.

Yes: "E: Go left 4, down 5 → (-4, -5)"

Similarly, B is (-3,6)

So distance is √[( -3 - (-4) )^2 + (6 - (-5))^2] = √[1^2 + 11^2] = √122

But perhaps in the context of the worksheet, they might accept 11.0 or something, but I think we should write the exact value.

Wait — maybe I made a mistake in coordinates.

Let me list all points again carefully based on typical grid reading:

Assume the grid has x from -6 to 6, y from -6 to 6.

Point A: x=-4, y=3 → (-4,3)
Point B: x=-3, y=6 → (-3,6)
Point C: x=3, y=1 → (3,1)
Point D: x=3, y=6 → (3,6)
Point E: x=-4, y=-5 → (-4,-5)
Point F: x=5, y=4 → (5,4)
Point G: x=3, y=-3 → (3,-3)
Point H: x=-2, y=-2 → (-2,-2)

All seem correct.

For distance between B and E:

Use distance formula: d = √[(x2-x1)^2 + (y2-y1)^2]

Let B be (x1,y1) = (-3,6), E be (x2,y2) = (-4,-5)

d = √[ (-4 - (-3))^2 + (-5 - 6)^2 ] = √[ (-1)^2 + (-11)^2 ] = √[1 + 121] = √122

So answer is √122.

But perhaps the worksheet expects a numerical approximation? Or maybe I need to leave it as is.

Looking at the other answers, they are integers, so maybe I have a mistake.

Another idea: Perhaps "distance" in this context means the number of grid lines crossed or something, but that's not standard.

Or maybe they want the sum of absolute differences? |Δx| + |Δy| = 1 + 11 = 12

That is called Manhattan distance, and sometimes used in grids.

In many elementary contexts, especially if not taught distance formula yet, they might mean that.

Let me check the level: The worksheet is titled "Coordinate Graphing", and asks for quadrants and distances — likely 6th or 7th grade.

In 6th grade, they often teach distance on horizontal/vertical lines, and for diagonal, they might not cover Pythagoras yet.

But in this case, for B and E, it's not horizontal or vertical.

Perhaps the problem intends for us to use the distance formula, and √122 is acceptable.

But let's see question 5: "The point located at (-3, -2) is _______" — which is not one of the labeled points, so we say "none" or "not labeled".

Back to Q3.

I recall that in some curricula, when they say "distance" on a coordinate plane without specifying, and if it's not aligned, they expect the Euclidean distance.

But to be safe, let's calculate both.

Euclidean: √122 ≈ 11.045

Manhattan: 12

Now, looking at the grid, from B to E, if you go left 1 and down 11, the straight line is hypotenuse.

But perhaps for this level, they want the actual distance using formula.

I think I should go with √122, but let's see if there's a better way.

Wait — perhaps I miscalculated the coordinates.

Let me visualize:

Point B: (-3,6) — that's 3 left, 6 up.

Point E: (-4,-5) — 4 left, 5 down.

So from B to E: move 1 unit left (from x=-3 to x=-4), and 11 units down (from y=6 to y=-5).

Yes.

Distance = sqrt(1^2 + 11^2) = sqrt(1+121) = sqrt(122)

I think we have to box that.

But let's proceed and come back.

Question 4: Quadrant of point B

B = (-3,6) → x negative, y positive → Quadrant II

✔ Answer: II

Question 5: The point located at (-3, -2) is _______

Look at our points:

A(-4,3), B(-3,6), C(3,1), D(3,6), E(-4,-5), F(5,4), G(3,-3), H(-2,-2)

Is any point at (-3,-2)? No.

H is at (-2,-2), not (-3,-2).

So no labeled point is at (-3,-2).

Answer: none or not labeled.

Probably "none" or "there is no point" but since it says "is _______", likely "none" or leave blank, but I think "none" is fine.

In some worksheets, they might say "not shown" but I think "none" is okay.

Now back to Q3.

Perhaps I can check if the distance is asked in a different way.

Another thought: Maybe "distance" means the length along the grid, but that doesn't make sense.

Or perhaps they want the difference in x and y separately, but the question says "the distance", implying scalar.

I recall that in some problems, if it's not specified, and for simplicity, they might expect the Manhattan distance for grid problems.

Let me search my memory: In Khan Academy or similar, for 6th grade, when introducing coordinates, they often only do horizontal and vertical distances, and for diagonal, they might avoid or use Pythagoras later.

But here, since it's included, and other questions are basic, perhaps for Q3, they intend for us to realize it's not aligned and use formula.

But sqrt(122) is ugly.

Let me calculate the numerical value: sqrt(121) = 11, sqrt(122) ≈ 11.045, so approximately 11.0, but not exact.

Perhaps I have a coordinate wrong.

Let me double-check point E.

In the initial description: "E: Go left 4, down 5 → (-4, -5)"

But is down 5 from origin? Yes, y=-5.

Point B: left 3, up 6 → (-3,6)

Yes.

Perhaps the grid is counted differently, but unlikely.

Another idea: Maybe "distance between B and E" is meant to be the shortest path on the grid, which would be |Δx| + |Δy| = 1 + 11 = 12.

And in many real-world grid contexts, like city blocks, that's used.

Moreover, in the answer choices or expectations, 12 is nice number.

Whereas sqrt(122) is not.

Also, for Q1, it was vertical, so 9, which is |6 - (-3)| = 9, correct.

For Q3, if they wanted Euclidean, it would be unusual for this level without calculator.

So perhaps they mean Manhattan distance.

Let me see the worksheet title: "Coordinate Graphing" — and it's from 15Worksheets.com, which is for K-12.

Upon quick mental search, I recall that in some 6th grade materials, "distance" on coordinate plane for non-aligned points is not covered, or they use the formula later.

But to resolve, let's look at question 5: (-3,-2) — which is close to H(-2,-2), but not the same.

Perhaps for Q3, the intended answer is 12, using |x1-x2| + |y1-y2|.

I think for safety, since this is likely middle school, and to match the integer answers, I'll go with Manhattan distance for Q3.

So | -3 - (-4) | + | 6 - (-5) | = |1| + |11| = 1 + 11 = 12

Yes.

In many educational contexts for younger students, "distance" in grid problems means the sum of horizontal and vertical moves.

So I'll use that.

So Q3: 12

Now, to confirm, let's see if there's any other clue.

Question 1 was vertical, so only y-difference, which is fine.

For B and E, if they wanted Euclidean, it would be specified or taught.

So I think 12 is intended.

Final decision: Use Manhattan distance for Q3.

So answers:

Coordinates:

A(-4, 3)
B(-3, 6)
C(3, 1)
D(3, 6)
E(-4, -5)
F(5, 4)
G(3, -3)
H(-2, -2)

Questions:

1) Distance D to G: |6 - (-3)| = 9 (since same x)
2) Quadrant of H: (-2,-2) → III
3) Distance B to E: | -3 - (-4) | + | 6 - (-5) | = 1 + 11 = 12
4) Quadrant of B: (-3,6) → II
5) Point at (-3,-2): none of the labeled points, so "none" or "not listed"

For Q5, since it says "is _______", and no point is there, probably "none" or leave blank, but I think "none" is fine.

In some formats, they might say "there is no point" but I'll put "none".

Now, to write final answer.

First, the ordered pairs:

A( -4 , 3 )
B( -3 , 6 )
C( 3 , 1 )
D( 3 , 6 )
E( -4 , -5 )
F( 5 , 4 )
G( 3 , -3 )
H( -2 , -2 )

Then:

1) 9
2) III
3) 12
4) II
5) none

For Q5, to be precise, since the question is "The point located at (-3, -2) is _______", and no letter is assigned, so "none" or "not labeled". I think "none" is sufficient.

Some might say "no point" but "none" is clear.

Now, box the final answer.

The user wants the final answer after reasoning.

So I'll compile.

Final Answer:

Ordered pairs:
A(-4, 3), B(-3, 6), C(3, 1), D(3, 6), E(-4, -5), F(5, 4), G(3, -3), H(-2, -2)

1) 9
2) III
3) 12
4) II
5) none

But to match the format, perhaps list them as per the worksheet.

Since the worksheet has blanks for A to H, and then questions 1-5.

In the response, I should provide all.

But the final answer section should contain the complete solution.

Perhaps write:

The ordered pairs are:
A: (-4, 3)
B: (-3, 6)
C: (3, 1)
D: (3, 6)
E: (-4, -5)
F: (5, 4)
G: (3, -3)
H: (-2, -2)

Answers to questions:
1) 9
2) III
3) 12
4) II
5) none

Yes.

For Q3, I decided on 12 using Manhattan distance, as it's more appropriate for this level and gives integer answer.

If it were Euclidean, it would be sqrt(122), but I think 12 is intended.

To confirm, let's see the distance between other points.

For example, from B to D: B(-3,6), D(3,6) — same y, distance |3 - (-3)| = 6, which is horizontal.

From D to G: vertical, 9.

From B to E: if they wanted Euclidean, it would be unusual.

I think 12 is correct for this context.

So final answer.