Point Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Point.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

An exact location in space with no size, length, or width—zero dimensions; named with a capital letter.

The tip of a pencil or a dot on a map. Position only, no width or length.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A point marks an exact position in space, with zero length, width, or thickness.

Common stuck point: The procedure for point is the easy part; the trap is treating a point as a small dot with size. Asking "Am I naming just a location, with no length, width, or size?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I naming just a location, with no length, width, or size?

Worked Examples

Example 1

easy
Plot the point (3,2)(3, 2) on a coordinate grid and describe its location.

Answer

The point (3,2)(3, 2) is 3 units right and 2 units up from the origin.

First step

1
Step 1: Start at the origin (0,0)(0, 0).

Full solution

  1. 2
    Step 2: Move 3 units to the right along the x-axis.
  2. 3
    Step 3: Move 2 units up along the y-axis.
  3. 4
    Step 4: Mark that location with a dot — this is the point (3,2)(3, 2).
A point has no size, no length, no area — it is simply a location in space. On a 2D coordinate grid, every point is uniquely identified by an ordered pair (x,y)(x, y).

Example 2

medium
Points A(1,1)(1,1), B(4,1)(4,1), and C(4,5)(4,5) are three corners of a rectangle. What are the coordinates of the fourth corner D?

Example 3

easy
A ladybug has these spots: ∙  ∙  ∙  ∙\bullet \; \bullet \; \bullet \; \bullet. How many spots?

Example 4

medium
A circle is drawn. A circle has no corners. How many corner points does a circle have?

Example 5

easy
A hexagon has 6 corners. Each corner is a point. How many corner points does a hexagon have?

Example 6

easy
Maya draws a line segment from point AA to point BB. How many endpoints does her line have?

Example 7

medium
Liam puts a dot on the left side of a paper and another dot on the right side. How many points did Liam draw?

Example 8

easy
A hexagon has 6 sides. How many vertices does it have?

Example 9

easy
A rectangle has 4 vertices. A triangle has 3 vertices. How many vertices do they have altogether?

Example 10

medium
Two streets cross each other once, and one of those streets crosses a third street at a different spot. How many intersection points are there?

Example 11

easy
Plot the point (3,2)(3, 2) on a grid. Describe how you find its spot.

Example 12

easy
Leo plots points A(1,1)A(1, 1) and B(1,4)B(1, 4) on a grid. Are these points on the same column or row?

Example 13

hard
Theo plots points (1,2)(1, 2), (4,2)(4, 2), and (4,6)(4, 6) on a grid. The three points are corners of a rectangle. Find the fourth corner, then count how many steps make up the bottom side.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
What are the coordinates of the origin on a standard coordinate grid?

Example 2

hard
In 3D space, describe the point (2,−3,5)(2, -3, 5). How does adding a third coordinate change what a point represents compared to 2D?

Example 3

easy
How many dimensions does a point have?

Example 4

easy
How are points usually named in geometry?

Example 5

easy
Does a point have any length?

Example 6

easy
How many points are needed to draw exactly one straight line?

Example 7

easy
A point is at location (3,5)(3, 5). What is its xx-coordinate?

Example 8

easy
What is the name of the point (0,0)(0, 0) on a coordinate grid?

Example 9

easy
Can two different points be at the exact same location?

Example 10

easy
On a number line, the point at 77 and the point at 22 are how far apart?

Example 11

medium
Three points all lie on one straight line. What word describes them?

Example 12

medium
Point MM is the midpoint of segment from (2,0)(2, 0) to (8,0)(8, 0). Find MM.

Example 13

medium
How many distinct lines can be drawn through a single point?

Example 14

medium
Points A(1,1)A(1,1) and B(1,5)B(1,5) are given. Are they on a vertical or horizontal line?

Example 15

medium
Four points are placed so that no three are collinear. How many distinct lines do they determine?

Example 16

medium
Why do we draw a point as a dot even though a true point has no size?

Example 17

medium
Point P(4,2)P(4, 2) is reflected across the yy-axis. Find the image.

Example 18

medium
Points A(0,0)A(0,0), B(4,0)B(4,0), C(4,3)C(4,3) are three corners of a rectangle. Find the fourth corner.

Example 19

challenge
Find the distance between points A(1,2)A(1, 2) and B(4,6)B(4, 6).

Example 20

challenge
How many points are needed to guarantee that at least two of them are collinear, if any two points are always collinear? Restate the real question and answer it.

Example 21

challenge
Five points lie on a circle. How many distinct chords (segments joining two of them) can be drawn?

Example 22

challenge
Point M(3,4)M(3, 4) is the midpoint of segment ABAB. If A=(1,2)A = (1, 2), find BB.

Example 23

easy
You see a dot like this: ∙\bullet. How many dots?

Example 24

easy
You see ∙  ∙  ∙\bullet \; \bullet \; \bullet. How many dots?

Example 25

easy
How many dots? ∙  ∙\bullet \; \bullet

Example 26

easy
A triangle has 3 corners. Each corner is a point. How many points does a triangle have?

Example 27

medium
A square has 4 corners. Each corner is a point. How many points does a square have?

Example 28

medium
Two friends each put 1 dot on a paper. How many dots in all?

Example 29

hard
A triangle has 3 corner points. A square also has corner points. Which one has more corner points, a triangle or a square?

Example 30

easy
A rectangle has corners at each end. How many corner points does a rectangle have?

Example 31

easy
A line has 2 ends. Each end is called an endpoint. How many endpoints does a line segment have?

Example 32

easy
How many dots? ∙  ∙  ∙  ∙  ∙  ∙  ∙\bullet \; \bullet \; \bullet \; \bullet \; \bullet \; \bullet \; \bullet

Example 33

medium
A triangle has 3 corner points. A rectangle has 4 corner points. How many corner points do they have together?

Example 34

medium
Owen drew 2 separate line segments. Each segment has 2 endpoints. How many endpoints are there in all?

Example 35

hard
Ava has a triangle and a square. She marks every corner with a dot. How many dots does she draw in all?

Example 36

easy
A polygon has a corner at each turn. The corners are called vertices. How many vertices does a triangle have?

Example 37

easy
How many vertices does a square have?

Example 38

easy
Two roads cross like a ++. The spot where they meet is called an intersection point. How many intersection points are there?

Example 39

medium
A polygon has 5 vertices. How many sides does it have?

Example 40

medium
A house drawing has a square base (44 vertices) with a triangle roof on top sharing the top side. How many vertices are in the whole house outline?

Example 41

hard
Rosa draws a hexagon and a triangle that do not touch. How many vertices are there in all?

Example 42

easy
On a grid, the point (2,3)(2, 3) means go 2 right and 3 up from the corner (0,0)(0, 0). What does (4,1)(4, 1) mean?

Example 43

easy
Where is the point (0,0)(0, 0) on a grid?

Example 44

easy
A point is 5 steps to the right of the origin and 2 steps up. Write its coordinates.

Example 45

medium
The point (4,3)(4, 3) is on a grid. How far is it from the point (0,3)(0, 3)? (Both are on the same row.)

Example 46

medium
Mia plotted points (2,1)(2, 1), (2,2)(2, 2), (2,3)(2, 3), and (2,4)(2, 4). What pattern do you see?
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Related Concepts

LineCoordinate Plane