Download - 11 X1 T05 07 Angle Between Two Lines
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Angle Between Two Lines
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Angle Between Two Linesy
x
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Angle Between Two Linesy
x
1l
1
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Angle Between Two Linesy
x
1l
1
1 1 1 has slope tanl m
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Angle Between Two Linesy
x
1l
1
1 1 1 has slope tanl m 2l
2
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Angle Between Two Linesy
x
1l
1
1 1 1 has slope tanl m 2l
2
2 2 2 has slope tanl m
![Page 7: 11 X1 T05 07 Angle Between Two Lines](https://reader035.vdocuments.us/reader035/viewer/2022062406/55895daed8b42a643f8b46be/html5/thumbnails/7.jpg)
Angle Between Two Linesy
x
1l
1
1 1 1 has slope tanl m 2l
2
2 2 2 has slope tanl m
![Page 8: 11 X1 T05 07 Angle Between Two Lines](https://reader035.vdocuments.us/reader035/viewer/2022062406/55895daed8b42a643f8b46be/html5/thumbnails/8.jpg)
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
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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
![Page 10: 11 X1 T05 07 Angle Between Two Lines](https://reader035.vdocuments.us/reader035/viewer/2022062406/55895daed8b42a643f8b46be/html5/thumbnails/10.jpg)
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
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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
![Page 12: 11 X1 T05 07 Angle Between Two Lines](https://reader035.vdocuments.us/reader035/viewer/2022062406/55895daed8b42a643f8b46be/html5/thumbnails/12.jpg)
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
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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
![Page 14: 11 X1 T05 07 Angle Between Two Lines](https://reader035.vdocuments.us/reader035/viewer/2022062406/55895daed8b42a643f8b46be/html5/thumbnails/14.jpg)
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
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2000 Extension 1 HSC Q1b)e.g. Find the acute angle between the lines
1 2 1 and 1
3y x y x
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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
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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
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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
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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
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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.
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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
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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
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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
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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
![Page 25: 11 X1 T05 07 Angle Between Two Lines](https://reader035.vdocuments.us/reader035/viewer/2022062406/55895daed8b42a643f8b46be/html5/thumbnails/25.jpg)
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
![Page 26: 11 X1 T05 07 Angle Between Two Lines](https://reader035.vdocuments.us/reader035/viewer/2022062406/55895daed8b42a643f8b46be/html5/thumbnails/26.jpg)
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
![Page 27: 11 X1 T05 07 Angle Between Two Lines](https://reader035.vdocuments.us/reader035/viewer/2022062406/55895daed8b42a643f8b46be/html5/thumbnails/27.jpg)
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
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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
![Page 29: 11 X1 T05 07 Angle Between Two Lines](https://reader035.vdocuments.us/reader035/viewer/2022062406/55895daed8b42a643f8b46be/html5/thumbnails/29.jpg)
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
![Page 30: 11 X1 T05 07 Angle Between Two Lines](https://reader035.vdocuments.us/reader035/viewer/2022062406/55895daed8b42a643f8b46be/html5/thumbnails/30.jpg)
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
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Exercise 14E; 1ac, 2bdf, 4, 7, 8, 10, 11a, 15*