Coordinate Geometry

Definition Coordinate grid – a grid used to locate a point

by its distances from 2 intersecting straight lines.

1

32

45

0

6

1 2 3 4 50 6

Definition x axis – a horizontal number line on a

coordinate grid.

1 2 3 4 50 6 x

Definition y axis – a vertical number line on a coordinate

grid.

12345

0

6

y

Definition Coordinates – an ordered pair of numbers that give

the location of a point on a grid.

(3, 4)

12345

0

6

1 2 3 4 50 6

(3,4)

Hint The first number is always the x or first letter in

the alphabet. The second number is always the y the second letter in the alphabet.

1

32

45

0

6

1 2 3 4 50 6

(3,4)

How to Plot Ordered Pairs Step 1 – Always find the x value first, moving

horizontally either right (positive) or left (negative).

1

32

45

0

6

1 2 3 4 50 6

(2, 3)y

x

How to Plot Ordered Pairs Step 2 – Starting from your new position find the y

value by moving vertically either up (positive) or down (negative).

1

32

45

0

6

1 2 3 4 50 6

(2, 3)(2,3)y

x

How to Find Ordered Pairs Step 1 – Find how far over horizontally the point is

by counting to the right (positive) or the left (negative).

1

32

45

0

6

1 2 3 4 50 6

(5, 4)y

x

How to Find Ordered Pairs Step 2 – Now count how far vertically the point is

by counting up (positive) or down (negative).

1

32

45

0

6

1 2 3 4 50 6

(5,4)y

x

What is the ordered pair?

1

32

45

0

6

1 2 3 4 50 6

(3,5)

y

x

What is the ordered pair?

1

32

45

0

6

1 2 3 4 50 6

(2,6)

y

x

What is the ordered pair?

1

32

45

0

6

1 2 3 4 50 6

(4,0)

y

x

Quadrants

There are 4 quadrants.

Four Quadrants Grid If the x is negative you move to the left of the

0.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

x = -2y

x

Four Quadrants Grid If the y is negative you move down below the

zero.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

y = -3y

x

How to Plot in 4 Quadrants Step 1 - Plot the x number first moving to the

left when the number is negative.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(-3, -2)(-3, -2) y

x

How to Plot in 4 Quadrants Step 2 - Plot the y number moving from your

new position down 2 when the number is negative.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(-3, -2)(-3, -2)y

x

How to Plot in 4 Quadrants When x is positive and y is negative, plot the

ordered pair in this manner.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(2, -2)(2, -2)y

x

How to Plot in 4 Quadrants When x is negative and y is positive, plot the

ordered pair in this manner.

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(-2, 2)(-2, 2)

y

x

Plot This Ordered Pair

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(-3, -3)(-3, -3)y

x

Plot This Ordered Pair

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(-1, 2)(-1, 2)y

x

Plot This Ordered Pair

-2

0-1

12

-3

3

-2 -1 0 1 2-3 3

(1, -1)(1, -1)y

x

Linear Graphsby Mausmi Jadhav

SLOPE

Mausmi Jadhav Khan

SlopeSlope• Slope is the steepness of a line.• It is represented by rise over run.• Formula:

12

12xxyym

Mausmi Jadhav Khan

SlopeSlope describes the direction of a line.

Mausmi Jadhav Khan

Special SlopesSpecial Slopes • Horizontal lines

– Slope = zero• Vertical lines

– Slope = undefined• Parallel lines

– Slopes are the same.• Intersecting lines

– Slopes are different and not perpendicular.• Perpendicular lines

– Slopes are the negative reciprocal of each other.

Slope (m)

NEGATIVE SLOPE (-)

POSITIVE SLOPE (+) Mausmi Jadhav Khan

Sign of the Slope

Which have a positive slope?

GreenBlue

Which have a negative slope?

RedPinkOrange

Undefined

ZeroSlope

Mausmi Jadhav Khan

Slope of a Line

x

y This line has a slope.

Take two points on this line.x2, y2

x1, y1

Rise = vertical distance

Run = horizontal distance

Slope (m) = rise = y2 – y1

run x2 – x1

Name the points.

Mausmi Jadhav Khan

Step – by – Step GuideVisual Instruction

Mausmi Jadhav Khan

Find the slope of the given line:(3, -8) (-5, 0) x1, y1 x2, y2

To find slope:

m = y2 – y1

x2 – x1

= 0 - - 8 -5 – 3 = 8 -8

Use abc on the calculator

8 _| -8

m = -1

1 mark to write the formula

1 mark to substitute values

1 mark to evaluate values

1 mark for answer

x-axis

y-axis

Find the slope between (-3, 6) and (5, 2)

RiseRun

-48

-12

= =

(-3, 6)

(5, 2)

Calculate the slope between (-3, 6) and (5, 2)

12

12

xxyym

)3-()5()6()2(

m

84-

21-

x1 y1 x2 y2

We use the letter mto represent slope

m

Mausmi Jadhav Khan

Find the Slopes

(5, -2)

(11, 2)

(3, 9)

12

12

xxyym

87

31192

1

mBrown

64

511)2-(2

2

m

Orange

211

3592-

3

mGreen

Mausmi Jadhav Khan

Find the slope between (5, 4) and (5, 2).

12

12

xxyym

)5()5()4()2(

m02-

STOP

This slope is undefined.

x1 y1 x2 y2

Mausmi Jadhav Khan

x

y

Find the slope between (5, 4) and (5, 2).

RiseRun

-20

Undefined= =

Find the slope between (5, 4) and (-3, 4).

12

12

xxyym

)5()3-()4()4(

m8-0

This slope is zero.

x1 y1 x2 y2

0

Mausmi Jadhav Khan

x

y

RiseRun

0-8

Zero= =

Find the slope between (5, 4) and (-3, 4).

From these results we can see...

The slope of a vertical line is undefined.

The slope of a horizontal line is 0.

Mausmi Jadhav Khan

POINT-SLOPE FORM

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Point – Slope Form

y – y1 = m (x – x1)

y2 – y1 = m (x2 – x1)REPLACE “2”

Mausmi Jadhav Khan

Point – Slope Form

y – y1 = m (x – x1)

slope

y - coordinate x - coordinate

Mausmi Jadhav Khan

Step – by – Step GuideVisual Instruction

Mausmi Jadhav Khan

Write the point – slope form of the equation

y – 6 = 2(x – 1)

slope

y - coordinate x - coordinate

Answer:

m = 2 and (1, 6)

y + 4 = 2(x – 8) 5

Answer:

m = 2 and (8, -4)

5 Mausmi Jadhav Khan