1. Intersection of Straight lines
Objectives
To be able to find the intersection Pt of 2 lines
To solve simultaneous equations
To solve the intersection of a curve and a line
To Sketch some specific types of curve
You should know how to find the equation of a line (from the previous lesson)
31 May, 2019
INTO Foundation L6 MH

2. Find the area of the triangle ABC
How do we do this ??
Find which line is which
Solve equations for ABC
Find Perpendicular line to BC
through A
31 May, 2019
INTO Foundation L6 MH

3. Solve for coordinates of A,B,C
Pt A Intersection of
y = 2x
y = -2x
2y= Add to remove x y=
x=(5.5 – 5)/ Subst y into 1.
x= 0.25
A = (0.25, 5.5)
31 May, 2019
INTO Foundation L6 MH

4. Solve for coordinates of A,B,C
Pt B Intersection of
y = x
y = -2x
0 = x Subtract to remove y
3.5= x
x=3.5/1.25
x= Subst x into (y=-5.6+6)
y= 0.40
B = (2.80, 0.40)
31 May, 2019
INTO Foundation L6 MH

5. Solve for coordinates of A,B,C
Pt C Intersection of
y = x
y = 2x
0 = x Subtract to remove y
2.5= x
x=2.5/-2.75
x= (~-10/11) Subst x into 1. (y=30/44+2.5)
y= (378/99 or 42/11)
C = (-10/11, 42/11)
31 May, 2019
INTO Foundation L6 MH

6. Found A,B,C A (0.25,0.55) C(-10/11, 43/11) B(2.80,0.40)
Find the line that is perpendicular to BC
through the point A
31 May, 2019
INTO Foundation L6 MH

7. Find Pt D D y = 4/3x +0.217 Grad BC is -0.75 Grad AD is +4/3 m1m2=-1
AD is y = 4/3x +c through A is
0.55=4/3(1/4)+c => c=
31 May, 2019
INTO Foundation L6 MH

8. Find Pt D Pt C Intersection of y = -0.75x + 2.50 1. y = 1.33 + 2.17 2.
To eliminate mult eqn1.x1.33 eqn 2.x0.75
1.33y = x
0.75y = x
2.08y =
y= /2.08 = Subst into 2.
x = (0.75(2.08) )/ =
D= (0.157, 2.38)
31 May, 2019
INTO Foundation L6 MH

9. Now Find Pt D
Area
For a triangle this is ½ x base x Perpendicular height
So ½ x BC x AD C = (-10/11, 42/11)
B(2.80,0.40)
D= (0.157, 2.38)
Length of BC is [(-10/11-2.8)2 + (42/ )2]1/2 = 5.04
Length of AD is [( )2 + ( )2] = 3.12
So Area is 0.50 x 5.04 x 3.12 = 7.9m2 (1 dec pl)
A ≡ (0.25, 5.5)
31 May, 2019
INTO Foundation L6 MH

10. Exercises Do worksheet If you finish do the following
Plot on graph paper on the same graph the curves :
y = x2
y = x3
y = 1/x
y = 1/x2
y = x4
31 May, 2019
INTO Foundation L6 MH