Embed Size (px)
Citation preview
MATHEMATICS
TOPIC : COORDINATE
GEOMETRY Presented by :
UMI KALSOM BINTI ABDOL RAHAMANUMI KALSOM BINTI ABDOL RAHAMAN
870728-04-5308
Distance
Mid-Point
Point dividing segment with ratio m:n
GEOMETRY COORDINATEGEOMETRY COORDINATE
General Information General Information
• General Equation for straight line
y = mx + c
• Gradient, m = y2-y1 x2-x1
• 2 Parallel straight line have same gradient
• 2 lines perpendicular, m1m2 = -1
GEOMETRY COORDINATEGEOMETRY COORDINATE
a) Distance
• How to find the distance between two point
B (x2,y2)
A (x1,y1)
Line AB = (X1-X2)2 + (Y1-Y2)2
• Example 1
Given P(3,2), Q(7,5), find the distance between point P and Q.
Answer :
Let (x1,y1) = (7,5) and (x2,y2)= (3,2)
PQ = (X1-X2)2 + (Y1-Y2)2
= (7-3)² + (5-2)²
= 4² + 3²
= 5 unit
Q (7,5)
P (3,2)
GEOMETRY COORDINATEGEOMETRY COORDINATE
b) Mid-Point
• How to find the midpoint of two points
R = midpoint
B (x2,y2)
A (x1,y1)
Mid Point = x1 + x2 , y1 + y2
2 2
R
• Example 2
Find the midpoint coordinates for AB lines
A( 5,7) B( 3,-1)
Answer:
= 5+3 7 + (-1)
2 2
= ( 4 , 3 )
AB = x1 + x2 , y1 + y2
2 2
B (3,-1)
A (5,7)
• Example 3
Given M (a, -3), N (-4, b) and the midpoint is (3,-2), find the value of a and b
Answer :
PQ = a+ (-4), -3 + b
2 2
a – 4 = 3 -3 +b = -2
2 2
a= 10 b = -1
c) Point that internally divides a line segment in the ratio m:n
GEOMETRY COORDINATEGEOMETRY COORDINATE
P (X1, Y1)
Q (X2, Y2)
n
m
R (a,b)
a = nx1 + mx2 , b = ny1 + my2
m+n m+n
• Example 4
P is a point that located in the straight line AB which A( 2,6) and B(8,0) with ratio AP: 2PB. Find the coordinate of P.
Answer :
AP : 2PB
A (2,6)
B (8,0)
P
2
1
a = nx1 + mx2 , b = ny1 + my2
m+n m+n
P = 1 x 2 + 2 x 8 , 1x6 + 2 x 0 2 + 1 2 + 1
= (6 , 2 )
So, coordinate P is (6,2).
Review
DISTANCE
Line AB = (X1-X2)2 + (Y1-Y2)2
RATIO m:n
a = nx1 + mx2 , b = ny1 + my2
m+n m+n
Mid Point = x1 + x2 , y1 + y2
2 2
Exercise Exercise 1. Find distance between the two points given:
a) A(-1,2),B(2,6)
b) G(4,-3), H( -5,-3)
c) C(15,4) , E(3,-1)
2. Find the midpoint of S(10,-3) and T(-4,-1) straight line.
3. Find the ratio point P(3,4) that divide straight line AB, A(-1,2) and B(9,7).
Thank You…
