LEVEL : FORM 2

LEVEL : FORM 2

LEARNING AREA:COORDINATESLEARNING OBJECTIVES:Understand and use the concept of distance between two points on a Cartesian planeLEARNING OUTCOMES:(i) Find the distance between two points with: (a) common y-coordinates(b) common x-coordinates

(ii) Find the distance between two points using Pythagoras theorem

HOW FAR IS YOUR SCHOOL FROM HOME ????

HOW DO YOU MEASURE THE DISTANCE ????

DO YOU KNOW WHAT ISDISTANCE ?LENGTHS BETWEEN TWO POINTS

AB = 6 -1 = 5 units1234A( 2, 1)B( 2, 6)5If x-coordinates are the same, the distance is the difference between their y coordinates Difference between the x coordinates ( the larger value minus the smaller value)COMMON X -COORDINATES26442CD = 1 (- 6) = 7 units1234D( 1, 2)C( -6, 2)567Difference between the y coordinates ( the larger value minus the smaller value)If y-coordinates are the same, the distance is the difference between their x coordinates COMMON Y-COORDINATES-2-4-621234 P( 2, 1)Q( 8, 9)52687654321DISTANCE BETWEEN TWO POINTSDraw a right angle triangle joining point P and point Q.

R2. Label the point of intersection of the two line as R3. Count/ calculate the number of units for length PR and QR

Find the distance between point P(2,1) and point Q(8,9)8 P( 2, 1)Q( 8, 9)DISTANCE BETWEEN TWO POINTS4. By using Pythagaros theorem, calculate the length of PQ.R

68 B( -2,3 )A ( 6, 9 )

DISTANCE BETWEEN TWO POINTSBy using Pythagaros theorem, calculate the length of PQ.9-3=66-(-2)=8DISTANCE BETWEEN TWO POINTSBy using Pythagaros theorem, find the distance between point A( , ) and point B( , )

9541

DISTANCE BETWEEN TWO POINTSBy using Pythagaros theorem, find the distance between point P( -1, -4 ) and point Q( -6 , 8 ).

TOPIC : COORDINATES

SUBTOPIC : MIDPOINTSLEARNING OUTCOMES:Identify the midpoint of a straight line joining two points.Find the coordinates of the midpoints of a straight line joining two points with:a. common y- coordinates.b. common x- coordinates.Find the coordinates of the midpoints of the line joining two points.Pose and solve problems involving midpoints.

UNDERSTAND & USE THE CONCEPT OF MIDPOINTS

IDENTIFY THE MIDPOINTS

15

10 KM5 km5 km*The tree is located in the middle of the drummer and the house. *What is the distance between the drummer and the tree?

*What is the distance between the house and the tree?16

10 KM5 km5 km

MIDPOINTThe midpoint is the point that divides a line into two equal parts17LETS IDENTIFY THE MIDPOINTS

0 unit2 units4 units

6 units

8 units10 unitsThe midpoint between drummer and Mr BThe midpoint between drummer and Dancing manmiceMr BThe midpoint between the mice and the treeHouse18The midpoint of AB = (3 , 4 )4A( 3, 0)B( 3, 8 )4When the x-coordinates of the two points are the same, then the x- coordinate of the midpoint remains the same.The y coordinate of the midpoint = 8+0 = 4 2MIDPOINT -COMMON X -COORDINATES264428M ( 3 , 4 )The midpoint of PQ = (-2,-2 )5Q( -2, -7)P( -2, 3 )5When the x-coordinates of the two points are the same, then the x- coordinate of the midpoint remains the same.The y coordinate of the midpoint = 3+(-7) = -2 2MIDPOINT -COMMON X -COORDINATES22-4-2- 2M ( -2 , -2 )-6The midpoint of PQ = = ( 5, 6 )3Q( 8, 6)P( 2, 6)3X coordinate of the midpoints = 2 + 8 = 5 2 When the y-coordinates of the two ponits are the same, the y- coordinate of the midpoint remains the sameMIDPOINT - COMMON Y-COORDINATES4268The midpoint of PQ = = ( -1, 2 )3B( 2, 2)A( -4, 2)3X coordinate of the midpoints = -4 + 2 = -1 2 When the y-coordinates of the two ponits are the same, the y- coordinate of the midpoint remains the sameMIDPOINT - COMMON Y-COORDINATES-2 2 4 -4 yx0COORDINATES OF THE MIDPOINT OF A LINE JOINING TWO POINTS

Q( 11, 8 )P( 1, 2 )8 + 2 = 5 21 + 11 = 6 256M(6, 5)

MIDPOINT OF A LINE JOINING TWO POINTSMIDPOINT =

P( 2, 1)Q( 8, 7) MFind the midpoint of PQ?Midpoint PQ=

YX0

EXERCISESBased onthe diagram:1.State the midpoint of AB.24 AR( 5,-3)264-2-4-2-4 C B y x8 QAnswers:

2.C is themidpoint of AD, statethecoordinates of D.3.Q is the midpoint ofPR, state the coordinates of P.1. (3, 2)2. D(1, 5)3. (-2, 1)EXERCISES24 AR( 5,-3)264-2-4-2-4 C B y x8 QAnswers:

Based onthe diagram:1.State the midpoint of ABCB2.If ABCD formsa rectangle,write the coordinates of D.3.Q is themidpoint of PR, state thecoordinates of P.1. a. (4,1) b. (4,3)

2. D(7,5) 3. P(-1,-1)EXERCISESIn the diagram, B is the midpoint of the straight line AC.What is the value of k?Answers:k = -2 yC( 6,k) xB( 2,5)A( -2,12)0The diagram showsa right-angled triangleABC.

The sides ABand AC are parallelto the y-axis and x-axis respectively.

The length of ABis 6 units.

If M is the midpoint of BC,

Find the value of p.B y xC( 3,1)A( 1, 1)M( 2,p )0

EXERCISESAnswers:p = 4CREATED BY:CHEONG SHU LINCHYE SOO FUENWAN ZAKIAH WAN MUSTAPHAZAIMIRA JAILANIZARINA MAAROF