Post on 05-Jan-2016
Presented by:
LEUNG Suk Yee
LEUNG Wing Yan
HUI Hon Yin
LED 3120B
PowerPoint Presentation
Target Audience : F.2 Students
Prerequisite knowledge :learnt about the distance between two points on the same horizontal line or on the same vertical line in a rectangle coordinate plane.
The use of slides : source of learning
LEUNG SUK YEE : Data Collection & Slide Production
LEUNG WING YAN : Data Collection & Slide Production
HUI Hon Yin:Slide Production & Layout Design
Hi, I am Joey. I am your guide in this presentation. Let explore the knowledge by click the below button.
GO!
1) Distance between any TWO points
2) Slope of a STRAIGHT line
3) PARALLEL lines
4) PERPENDICULAR lines
5) MC Questions
1.1 Distance between two points on the same horizontal line
y
x0
The Distance of AB:
AB = 4-1
= 3 unitsA(1,1) B(4,1)
1.2 Distance between two points on the same vertical line
y
x0
Distance of AC:
AC = 5-1
= 4 units
C(1,5)
A(1,1)
1.3 Distance between any two points y
x0
Then, do you know the distance between these two points ?
C(1,5)
B(4,1)
i) Draw a vertical line from A through C
ii) Draw a horizontal line from A through B
iii) Since ABC is right-angled triangle, do you remember that we can use the Pythagoras’ theorem to calculate the hypotenuse BC?
y
x0
C(1,5)
B(4,1)
A(1,1)
By the Pythagoras’ theorem,we have
BC 2 =AB 2 +AC 2
=3 2 +4 2
=9 +16
=25
∴BC =5
y
x0
C(1,5)
B(4,1)
A(1,1)
Why???
From the figure, we have
AB = x1 - x 2 and AC = y1 – y2
By Pythagoras’ theorem, we have
BC2 = AB2 + AC2
= (x1- x2 ) 2 + (y1 – y2 ) 2
1.4 Distance Formulay
x0
C(x2,y1)
B(x1,y2)A(x2,y2)
) y - (y ) x- (x 221
221 BC
BC2 = (x1 - x2 ) 2 + (y1 - y2 ) 2
= (4-1) 2 + (2-6) 2
= 3 2 + (-4) 2
= 25
∴ BC=5
y
x0
C(1,5)
B(4,1)
C(-1,4)
A(-2,0)B(2,-1)
y
x
Find the perimeter of ABC correct to 1 decimal place.
Solution :
Example 1
Time Remain
5 sec
Time Remain
3 sec
Time Remain
2 sec
Time Remain
1 sec
Time Remain
4 sec
AB2 =(-2 -2) 2 + 0-(-1) 2 =17
BC 2=2-(-1) 2 + (-1- 4) 2 =34
AC2 = -2 - (-1) 2 + (0-4) 2 =17
Perimeter of ABC
=AB + BC +AC
=
=14.1(correct to 1d.p.)
173417
Lines AB and CD represent two steep roads. Which road is steeper?
Obviously road CD is steeper than road AB.
But, can you tell the steepness of the roads?
2.1 Definition of Slope
A
B
D
C
We can determine in this way
Difference in x-
coordinates
Difference in y-
coordinates
(x 1 , y 2)
(x 1 , y 1)
(x 2 ,y 2)
A(x , y ) and B (x , y ) are two points on a straight line.
Difference in y- coordinates =y1-y2
Difference in corresponding x- coordinates=x1-x2
Hence, Slope of a line = y1-y2 / x1-x2
..
.P(2,3)
Q (12,9)
R (7,9)
Example 2
Answer:
Slope of PQ
= 3-9 / 2-12 = -6 / -10 = 3/5
Slope of PR
= 3-9 / 2-7 = -6 / -5 = 6/5
Find the slope of the lines PQ & PR
Time Remain
5 sec
Time Remain
4 sec
Time Remain
3 sec
Time Remain
2 sec
Time Remain
1 sec
Example 3
Answer:
Slope of XY
= 1-10 / 10-4 = -9 / 6 = -3 / 2
Slope of XZ
= 1-7 / 10-2 = -6 / 8 = -3 / 4
Find the slope of the lines XY & XZ
.
.Z(2,7)
Y (4,10)
X (10,1)
Time Remain
5 sec
Time Remain
4 sec
Time Remain
3 sec
Time Remain
2 sec
Time Remain
1 sec
From the above two example, we can conclude that:
(1) when a straight line rises from left to right, the slope of the line is a positive .
(2) when a straight line falls from left to right, the slope of the line is negative.
Line with positive slope
Line with negative slope
2.2 The Characteristics of slope
There is a pair of parallel lines.
What’s the different between there slope?
Slopes of Parallel Lines
Slope of AB
= 1-3 / 1-5
= -2 / -4
=1 / 5
A(1,1)
B(5,3)
C(-1,1)
D(2,2.5)
Slope of CD
= 1-2.5 / -1- 2
= (-3 / 2) / -3
= 1 / 2
So, Slope of AB = Slope of CD =1 / 2
In general,
If two lines are parallel, then their slopes are
equal.Conversely,
If two lines have same slope,then they are parallel.
A(3, -1)
B(4,3)
C(-2,-2)
D(-3/2,0)
Show that two straight lines AB and CD are parallel.
Answer:
Slope of AB = (-1-3)/3-4
= -4/-1 = 4
Slope of CD = (-2-0)/-2-(-3/2)
= -2/(-1/2)
= 4
Example 4
Since slope of AB = slope of CD,so AB and CD are parallel lines.
Time Remain
5 sec
Time Remain
4 sec
Time Remain
3 sec
Time Remain
2 sec
Time Remain
1 sec
D(1,6)
B(6,5)
C(5,0)A(0,1)
Slopes of Perpendicular Lines
There is a pair of perpendicular lines.
What’s the relationship between there slope?
D(1,6)
B(6,5)
C(5,0)A(0,1)
Slope of AB
= 5-1 / 6-0
= 4 / 6
= 2/3
Slope of CD
= 6-0 / 1-5
= 6 / -4
= -3/2
Slope of AB x Slope of CD
= 2/3 x (-3/2)
=-1
In general,
If two lines are perpendicular,then the product of their slopesare equal to -1.
Conversely,
If the product of their slopes are equal to -1,then they are perpendicular.
Example 5 Show that two straight lines AB and CD are perpendicular.
A(0,3)
B(-2,0)
C(-6,4)
D(0,0)
Answer:
Slope of AB = (3-0)/0-(-2)
= 3/2
Slope of CD = (4-0)/(-6)-0
= -4/6
= -2/3
∵Slope of AB x slope of CD =3/2 x (-2/3) =-1 ∴AB and CD are perpendicular.
Time Remain
5 sec
Time Remain
4 sec
Time Remain
3 sec
Time Remain
2 sec
Time Remain
1 sec
1. Find the perimeter of a square if X(- 3,8) and Y(2,-4) are two adjacent vertices of the square.
A. 13
B. 52
C. 169
2. In the figure, which line has the greatest slope?
A. L1
B. L2
C. L3x
y
L3 L2
L1
.
. .
.
(4,3)
(3,n)
(2,5)
(1,0)
A
C
B
D
x
y
3. In the figure, AB is parallel to CD. What is the value of n?
C. 8
B. -1
A. -2
4. Given two points M(2,0) and N(5,1). If P(3,b) is a point such that MP=MN, find b..
A. 3 only
B. 2 or -2
C. 3 or -3
.
.
D
(a,b)
(-1,-2)
C
A
Bx
y
5. In the figure, AB is perpendicular to CD. (a,b) and (-1,-2) are two points on CD. If the slope of AB is –1/2, express a in terms of b.
A. a=b/2
B. a=-b/2
C. a=2b+
3
END
Produced by
Leung Suk Yee 99736862
Leung Wing Yan 99688683
Hui Hon Yin 99530432
RIGHTLet‘ s try another question by click the below button
RIGHTLet‘ s try another question by click the below button
RIGHTLet‘ s try another question by click the below button
RIGHTLet‘ s try another question by click the below button
RIGHTWell done, You have finish
all the question!
13 is only the length of one side of the square, not the perimeter of the square.
Wrong
Don’t give up!
Let’s try it again.
169 is the area of the square, not the perimeter of the square
Wrong
Don’t give up!
Let’s try it again.
L1 is parallel to the x-axis, there is no difference in y-coordinates, therefore slope of L1 isSlope of L1 = 0/x1-x2= 0
Wrong
Don’t give up!
Let’s try it again.
L2 falls from left to right, the slope must be negative.
Wrong
Don’t give up!
Let’s try it again.
You may have some problems in using the slope formula.Slope formula = y1-y2 / x1-x2
Are you sure that you have put x1 ,x2 ,y1 and y2 in the right place of the formula ?
Wrong
Don’t give up!
Let’s try it again.
In fact, 9 can be the square of both 3 and -3.
Wrong
Don’t give up!
Let’s try it again.
The situation is MP =MN , not MP = PN.
Wrong
Don’t give up!
Let’s try it again.
You may make some mistakes in the process of calculation. Please be more careful.
Wrong
Don’t give up!
Let’s try it again.
The slope formula is y1-y2 / x1-x2 , not x1-x2 / y1-y2
Wrong
Don’t give up!
Let’s try it again.