LEARNING 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

DO YOU KNOW WHAT ISDISTANCE ?LENGTHS BETWEEN TWO POINTS

CD = 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 -2-4-62

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)26442

1234 P( 2, 1)Q( 8, 9)52687654321Draw 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)

P( 2, 1)Q( 8, 9)4. By using Pythagaros theorem, calculate the length of PQ.R68

B( -2,3 )A ( 6, 9 )By using Pythagaros theorem, calculate the length of PQ.9-3=66-(-2)=8

By using Pythagaros theorem, find the distance between point A( , ) and point B( , ).9542

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

TOPIC : COORDINATES

SUBTOPIC : MIDPOINTS

LEARNING 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

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?

10 KM5 km5 kmMIDPOINTThe midpoint is the point that divides a line into two equal parts

LETS IDENTIFY THE MIDPOINTS0 unit2 units4 units6 units8 units10 unitsThe midpoint between drummer and Mr BThe midpoint between drummer and Dancing manmiceMr BThe midpoint between the mice and the treeHouse

The 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 2264428M ( 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) = -2 222-4-2- 2M ( -2 , -2 )-6

The 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 same4268

The 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 same-2 2 4 -4

COORDINATES OF THE MIDPOINT OF A LINE JOINING TWO POINTSQ( 11, 8 )P( 1, 2 )8 + 2 = 5 21 + 11 = 6 256M(6, 5)

MIDPOINT OF A LINE JOINING TWO POINTS

MIDPOINT =

P( 2, 1)Q( 8, 7) MFind the midpoint of PQ?Midpoint PQ=YX0

Based 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)

Answers:

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)

In the diagram, B is the midpoint of the straight line AC.What is the value of k?Answers:k = -2

The 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 )0Answers:p = 4

CREATED BY:CHEONG SHU LINCHYE SOO FUENWAN ZAKIAH WAN MUSTAPHAZAIMIRA JAILANIZARINA MAAROF

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