11 x1 t05 07 angle between two lines

Angle Between Two Lines

Angle Between Two Linesy

x

Angle Between Two Linesy

x

1l

1

Angle Between Two Linesy

x

1l

1

1 1 1 has slope tanl m

Angle Between Two Linesy

x

1l

1

1 1 1 has slope tanl m 2l

2

Angle Between Two Linesy

x

1l

1

1 1 1 has slope tanl m 2l

2

2 2 2 has slope tanl m

Angle Between Two Linesy

x

1l

1

1 1 1 has slope tanl m 2l

2

2 2 2 has slope tanl m

Angle Between Two Linesy

x

1l

1 2 (exterior ) 1

1 1 1 has slope tanl m 2l

2

2 2 2 has slope tanl m

Angle Between Two Linesy

x

1l

1 2 (exterior )

1 2 1

1 1 1 has slope tanl m 2l

2

2 2 2 has slope tanl m

Angle Between Two Linesy

x

1l

1 2 (exterior )

1 2 1

1 1 1 has slope tanl m 2l

2

2 2 2 has slope tanl m

1 2tan tan

Angle Between Two Linesy

x

1l

1 2 (exterior )

1 2

1 2

1 2

tan tan

1 tan tan

1

1 1 1 has slope tanl m 2l

2

2 2 2 has slope tanl m

1 2tan tan

Angle Between Two Linesy

x

1l

1 2 (exterior )

1 2

1 2

1 2

tan tan

1 tan tan

1

1 1 1 has slope tanl m

1 2

1 21

m m

mm

2l

2

2 2 2 has slope tanl m

1 2tan tan

Angle Between Two Linesy

x

1l

1 2 (exterior )

1 2

1 2

1 2

tan tan

1 tan tan

1

1 1 1 has slope tanl m

1 2

1 21

m m

mm

2l

2

2 2 2 has slope tanl m

1 2tan tan

The acute angle between two lines with slopes and can be found using;

1m 2m

Angle Between Two Linesy

x

1l

1 2 (exterior )

1 2

1 2

1 2

tan tan

1 tan tan

1

1 1 1 has slope tanl m

1 2

1 21

m m

mm

2l

2

2 2 2 has slope tanl m

1 2tan tan

21

21

1tan

mmmm

The acute angle between two lines with slopes and can be found using;

1m 2m

2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines

1 2 1 and 1

3y x y x

2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines

1 2 1 and 1

3y x y x

31

21

31

2tan

2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines

1 2 1 and 1

3y x y x

31

21

31

2tan

2316

2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines

1 2 1 and 1

3y x y x

31

21

31

2tan

2316

1

2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines

1 2 1 and 1

3y x y x

31

21

31

2tan

2316

145

2005 Extension 1 HSC Q1f)45(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is

Find the possible values of m.

2005 Extension 1 HSC Q1f)45(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is

Find the possible values of m.

mm

313

45tan

2005 Extension 1 HSC Q1f)45(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is

Find the possible values of m.

mm

313

45tan

mm

313

1

2005 Extension 1 HSC Q1f)45(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is

Find the possible values of m.

mm

313

45tan

mm

313

1

mm 331

2005 Extension 1 HSC Q1f)45(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is

Find the possible values of m.

mm

313

45tan

mm

313

1

mm 331

mmmm 331 or 331

2005 Extension 1 HSC Q1f)45(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is

Find the possible values of m.

mm

313

45tan

mm

313

1

mm 331

mmmm 331 or 331

24 m

2005 Extension 1 HSC Q1f)45(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is

Find the possible values of m.

mm

313

45tan

mm

313

1

mm 331

mmmm 331 or 331

21m

24 m

2005 Extension 1 HSC Q1f)45(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is

Find the possible values of m.

mm

313

45tan

mm

313

1

mm 331

mmmm 331 or 331

21m

mm 33124 m

2005 Extension 1 HSC Q1f)45(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is

Find the possible values of m.

mm

313

45tan

mm

313

1

mm 331

mmmm 331 or 331

21m

mm 331

42 m

24 m

2005 Extension 1 HSC Q1f)45(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is

Find the possible values of m.

mm

313

45tan

mm

313

1

mm 331

mmmm 331 or 331

21m

mm 331

42 m

2m

24 m

2005 Extension 1 HSC Q1f)45(ii) The acute angle between the lines y = 3x + 5 and y = mx + 4 is

Find the possible values of m.

mm

313

45tan

mm

313

1

mm 331

mmmm 331 or 331

21m

mm 331

42 m

2m2or

21 mm

24 m

Exercise 14E; 1ac, 2bdf, 4, 7, 8, 10, 11a, 15*