• Prakash AdhikariIslington College, Kathmandu

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Pure Mathematics (P1)- 9709

Topic: Co-ordinate Geometry

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Lesson DescriptionIn this lesson, we will learn:• Distance between two points of a line segment• Mid point of the line segment joining two points• Gradient (Slope) of the line segment

– Gradient of Parallel lines– Gradient of Perpendicular lines

Compare with chart alongside..

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Y

X

A(x1,y1)

x1 x2

y1

y2 B(x2,y2)

Compare with chart alongside..

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Y

X

A(x1,y1

x1 x2

y1

y2 B(x2,y2)

Compare with chart alongside..

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Y

X

A(x1,y1)

x1 x2

y1

y2 B(x2,y2)

d

Compare with chart alongside..

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Y

X

A(x1,y1)

x1 x2

y1

y2 B(x2,y2)

d

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Y

X

A(x1,y1)

x1 x2

y1

y2 B(x2,y2)

(y2-y1)

(x2-x1)

d

• z

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Y

X

A(x1,y1)

x1 x2

y1

y2 B(x2,y2)

(y2-y1)

(x2-x1)

h

d

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Y

X

A(x1,y1)

x1 x2

y1

y2 B(x2,y2)

(y2-y1)

(x2-x1)

h

𝑑=√( x2 − x 1 )2+ ( y 2− y1 )2  

d

Example:• Distance between two points: A (9,7) and B(3,2)

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Units= 7.8102… Units

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Y

X

A(x1,y1)

x1 x2

y1

y2 B(x2,y2)

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Y

X

A(x1,y1)

x1 x2

y1

y2 B(x2,y2)

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Y

X

A(x1,y1)

x1 x2

y1

y2 B(x2,y2)

C

So, the co- ordinate of c (x,y)= [ ]15

Y

X

A(x1,y1)

x1 x2

y1

y2 B(x2,y2)

𝟏𝟐

(𝒙¿¿𝟏+𝒙𝟐)¿

𝟏𝟐

(𝒚 ¿¿𝟏+𝒚 𝟐)¿C

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Coordinate of Midpoint M = [ ]

Slope of the line:

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Definition of Slope

The slope of the line through the distinct points (x1, y1) and (x2, y2) is

Definition of Slope

The slope of the line through the distinct points (x1, y1) and (x2, y2) is Change in y

Change in x=

Rise

Run=y2 – y1

x2 – x1

(x1, y1)

x1

y1

x2

y2

(x2, y2)Risey2 – y1

Runx2 – x1

x

y

The steepness of a line, called the slope of the line. Slope compares the vertical change (the rise) to the horizontal change (the run) when moving from one fixed point to another along the line. A ratio comparing the change in y (the rise) with the change in x (the run) is used calculate the slope of a line.

Rise = 4

Run = 5

Slope=

m=

Sample Problems:

• Find the slope of the line thru the points given:(-3,-1) and (-2,4)

(-3,4) and (2,-2)

m4 1 2 3

5

15

m 2 4

2 3 6

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The Possibilities for a Line’s Slope

Positive Slope

x

y

m > 0

Line rises from left to right.

Zero Slope

x

y

m = 0

Line is horizontal.m is

undefined

Undefined Slope

x

y

Line is vertical.

Negative Slope

x

y

m < 0

Line falls from left to right.

Slope of second line m2

Slope of First line m1

Two lines are parallel if

m1=m2

The End