Ordered Pairs Examples in Math

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

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 ordered pair $(x, y)$ is a pair of numbers used to locate a point on the coordinate plane, where $x$ is the horizontal position and $y$ is the vertical position.

Like giving directions: go 3 blocks east, then 4 blocks north — the order matters because (3, 4) is a different spot than (4, 3).

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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: An ordered pair $(x,y)$ locates a point by its horizontal value first and vertical value second, so the order matters.

Common stuck point: The procedure for ordered pairs is the easy part; the trap is plotting up first then across. Asking "Am I naming a single point with a horizontal value first and a vertical value second?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I naming a single point with a horizontal value first and a vertical value second?

Worked Examples

Example 1

medium

Which quadrant contains

(-5, -3)

Answer

\text{III}

First step

Both coordinates are negative.

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Example 2

medium

Find the midpoint of

(2, 1)

and

(8, 7)

Find midpoint M of segment AB

Example 3

medium

List ordered pairs for

y = 2x

x = 0, 1, 2, 3

Ordered pairs on y = 2x at x = 0, 1, 2, 3

Example 4

hard

Find the distance between

(1, 2)

and

(4, 6)

Find the distance d between A(1,2) and B(4,6)

Example 5

hard

Triangle has vertices

(0,0)

(6,0)

(0,4)

. Find its area.

Find the area of this right triangle

Example 6

hard

Find the fourth vertex of a parallelogram with vertices

A(1,1)

B(5,1)

C(7,4)

where

D

is opposite

B

Find the fourth vertex D of the parallelogram (opposite B)

Example 7

challenge

Three vertices of a square are

(0,0)

(4,0)

(4,4)

. Find the fourth and the area.

Practice Problems

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

Example 1

easy

In the ordered pair

(4, 7)

, what is the

x

-coordinate?

Example 2

easy

(4, 7)

, what is the

y

-coordinate?

Example 3

easy

Are

(3, 5)

and

(5, 3)

the same point?

A(3,5) and B(5,3) plotted — are they the same point?

Example 4

easy

What ordered pair is the origin?

Example 5

easy

To plot

(2, 3)

, how far do you move right then up?

Move right 2, then up 3 to reach (2, 3)

Example 6

easy

Write the ordered pair for a point 5 right and 0 up from the origin.

Example 7

easy

Which quadrant sign pattern does

(+, +)

describe?

Example 8

easy

How many numbers are in an ordered pair?

Example 9

medium

Plot

(-3, 2)

: which quadrant is it in?

Which quadrant contains (−3, 2)?

Example 10

medium

A point is at

(x, 4)

and lies on the

y

-axis. Find

x

Example 11

medium

Give the ordered pair 2 units left of

(5, 3)

Example 12

medium

Points

(2, 1)

and

(2, 6)

— what kind of segment joins them?

Segment joining (2,1) and (2,6) — vertical or horizontal?

Example 13

medium

The midpoint of

(0,0)

and

(6, 8)

is which ordered pair?

Find the midpoint M of segment AB

Example 14

medium

A rectangle has corners

(0,0)

(5,0)

(5,3)

. Give the fourth corner.

Find the missing fourth corner of the rectangle

Example 15

medium

(a, 2)

and

(7, 2)

are 4 apart horizontally, find

a

(a < 7).

Example 16

medium

List the ordered pairs for

y = x

x = 0, 1, 2

Points on y = x at x = 0, 1, 2

Example 17

medium

Reflect

(3, 5)

over the

x

-axis. Give the new pair.

Reflect (3, 5) over the x-axis

Example 18

challenge

Three vertices of a parallelogram are

(0,0)

(4,0)

(1,3)

. Find the fourth (opposite

(4,0)

Find the fourth vertex D of the parallelogram

Example 19

challenge

Point

(p, q)

is in Quadrant III and 5 units from the origin along the line

y=x

. Find

(p,q)

Example 20

challenge

For what

k

are

(1,2)

(3, k)

(5, 10)

collinear?

Find k so that (3, k) is collinear with (1,2) and (5,10)

Example 21

easy

In the ordered pair

(8, 2)

, what is the

x

-coordinate?

Example 22

easy

(8, 2)

, what is the

y

-coordinate?

Example 23

easy

From the origin, how do you reach

(6, 4)

Example 24

easy

What ordered pair represents a point on the

x

-axis with

x = 7

Example 25

easy

(2, 9)

in Quadrant I?

Example 26

easy

Order matters: are

(1, 9)

and

(9, 1)

the same point?

Example 27

easy

Write the ordered pair for the origin.

Example 28

easy

Which quadrant has sign pattern

(-, +)

Example 29

medium

Give the ordered pair

3

units above

(2, 5)

Example 30

medium

What is the distance between

(1, 4)

and

(1, 9)

Find the distance d between (1,4) and (1,9)

Example 31

medium

What is the distance between

(3, 2)

and

(8, 2)

Find the distance d between (3,2) and (8,2)

Example 32

medium

Reflect

(4, -2)

over the

y

-axis. Give the new pair.

Reflect (4, −2) over the y-axis

Example 33

medium

Reflect

(3, 7)

over the

x

-axis.

Reflect (3, 7) over the x-axis

Example 34

medium

Points

(2,3)

(2,7)

(6,7)

are three corners of a rectangle. Find the fourth.

Find the missing fourth corner of the rectangle

Example 35

medium

(a, 3)

and

(7, 3)

are

5

apart and

a < 7

, find

a

Example 36

medium

Is the point

(4, 12)

on the line

y = 3x

Example 37

hard

Are

(1, 2)

(3, 6)

(5, 10)

collinear?

Example 38

hard

A rectangle has vertices

(1, 2)

and

(7, 6)

as opposite corners. Find the center.

Example 39

hard

Translate

(3, -2)

\langle -5, 4 \rangle

. Give the new pair.

Example 40

hard

(a, b)

is in Quadrant IV and

|a| = 3

|b| = 7

, find

(a, b)

Example 41

hard

Find

k

so that

(2, k)

is on the line

y = 3x - 1

Example 42

hard

Two points

(0,0)

and

(a, a)

are

\sqrt{50}

apart. Find positive

a

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Related Concepts

Number Line Coordinate Plane Linear Functions Function Tables and Graphs

Background Knowledge

These ideas may be useful before you work through the harder examples.

number linecoordinate plane