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)

19 April 2023 INTO Foundation L6 MH

Find the area of the triangle ABC

19 April 2023 INTO Foundation L6 MH

How do we do this ??1. Find which line is which2. Solve equations for ABC3. Find Perpendicular line to BC through A

A

B

C

Solve for coordinates of A,B,C

Pt A Intersection of

y = 2x + 5 1.

y = -2x + 6 2.

2y= 11 Add to remove x

y= 5.5 x=(5.5 – 5)/2 Subst y into 1. x= 0.25

A = (0.25, 5.5)

19 April 2023 INTO Foundation L6 MH

Solve for coordinates of A,B,C

Pt B Intersection of

y = -0.75x + 2.5 1.

y = -2x + 6 2.

0 = 1.25x -3.5 Subtract to remove y

3.5= 1.25x x=3.5/1.25 x= 2.80 Subst x into 2. (y=-5.6+6) y= 0.40

B = (2.80, 0.40)

19 April 2023 INTO Foundation L6 MH

Solve for coordinates of A,B,C

Pt C Intersection of

y = -0.75x + 2.5 1.

y = 2x + 5 2.

0 = -2.75x -2.5 Subtract to remove y

2.5= -2.75x x=2.5/-2.75 x= -0.9090 (~-10/11) Subst x into 1. (y=30/44+2.5) y= (35/11)

C = (-10/11, 35/11)

19 April 2023 INTO Foundation L6 MH

19 April 2023 INTO Foundation L6 MH

A (0.25,5.5)

B(2.80,0.40)

C(-10/11, 35/11)

Find the line that is perpendicular to BC through the point A

19 April 2023 INTO Foundation L6 MH

D

Grad BC is -0.75

Grad AD is +4/3

m1m2=-1

AD is y = 4/3x +c through A is

5.5=4/3(1/4)+c => c=5.16667

y = 4/3x + 31/6

5.5

35/11

Find Pt D

Pt C Intersection of

y = -0.75x + 2.50 1.

y = 1.33x + 5.17 2. To eliminate mult eqn1.x1.33 eqn 2.x0.75

1.33y = -0.9975x + 3.3250 3.

0.75y = 0.9975x + 3.8775 4. add(3+4)

2.08y = 7.2025 y= 7.7025/2.08 = 3.46 Subst into 2. x = (3.46 – 5.15)/1.33 = -1.29

19 April 2023 INTO Foundation L6 MH

D= (-1.29, 3.46)

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, 35/11)

B(2.80,0.40)

D= (-1.29, 3.46)

Length of BC is [(-10/11-2.8)2 + (35/11-0.40)2]1/2 = 4.64

Length of AD is [(3.46-5.5)2 + (-1.29-0.25)2] = 2.56

So Area is 0.50 x 4.64 x 2.56 = 5.9m2 (1 dec pl)

19 April 2023 INTO Foundation L6 MH

A ≡ (0.25, 5.5)

Exercises

Do worksheet

If you finish do the following

Plot on graph paper on the same graph the curves : 1. y = x2

2. y = x3

3. y = 1/x

4. y = 1/x2

5. y = x4

19 April 2023 INTO Foundation L6 MH