11x1 t05 06 line through point of intersection (2010)
TRANSCRIPT
Equation of a line through a point and intersection of
another two lines
Equation of a line through a point and intersection of
another two linese.g. Find the equation of the line that passes through the intersection of
2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2).
Equation of a line through a point and intersection of
another two linese.g. Find the equation of the line that passes through the intersection of
2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2).
2 1 03 5 9 0
x yx y
Equation of a line through a point and intersection of
another two linese.g. Find the equation of the line that passes through the intersection of
2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2).
2 1 03 5 9 0
x yx y
10 5 5
3 5 9x yx y
Equation of a line through a point and intersection of
another two linese.g. Find the equation of the line that passes through the intersection of
2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2).
2 1 03 5 9 0
x yx y
10 5 5
3 5 9x yx y
( )
Equation of a line through a point and intersection of
another two linese.g. Find the equation of the line that passes through the intersection of
2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2).
2 1 03 5 9 0
x yx y
10 5 5
3 5 9x yx y
( )
7 = 14x
Equation of a line through a point and intersection of
another two linese.g. Find the equation of the line that passes through the intersection of
2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2).
2 1 03 5 9 0
x yx y
10 5 5
3 5 9x yx y
( )
7 = 14x 2x
Equation of a line through a point and intersection of
another two linese.g. Find the equation of the line that passes through the intersection of
2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2).
2 1 03 5 9 0
x yx y
10 5 5
3 5 9x yx y
( )
7 = 14x 2x 2 2 1 0y
3y
Equation of a line through a point and intersection of
another two linese.g. Find the equation of the line that passes through the intersection of
2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2).
2 1 03 5 9 0
x yx y
10 5 5
3 5 9x yx y
( )
7 = 14x 2x 2 2 1 0y
3y the lines intersect at 2,3
Equation of a line through a point and intersection of
another two linese.g. Find the equation of the line that passes through the intersection of
2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2).
2 1 03 5 9 0
x yx y
10 5 5
3 5 9x yx y
( )
7 = 14x 2x 2 2 1 0y
3y the lines intersect at 2,3 3 2
2 113
m
Equation of a line through a point and intersection of
another two linese.g. Find the equation of the line that passes through the intersection of
2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2).
2 1 03 5 9 0
x yx y
10 5 5
3 5 9x yx y
( )
7 = 14x 2x 2 2 1 0y
3y the lines intersect at 2,3 3 2
2 113
m
12 13
y x
Equation of a line through a point and intersection of
another two linese.g. Find the equation of the line that passes through the intersection of
2x + y + 1= 0 and 3x + 5y – 9 = 0 and the point (1,2).
2 1 03 5 9 0
x yx y
10 5 5
3 5 9x yx y
( )
7 = 14x 2x 2 2 1 0y
3y the lines intersect at 2,3 3 2
2 113
m
12 13
y x
3 6 13 7 0
y xx y
Alternatively
Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c
Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c
2 1 3 5 9 0x y k x y
Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c
2 1 3 5 9 0x y k x y
1,2 : 2 1 2 1 3 1 5 2 9 0k
Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c
2 1 3 5 9 0x y k x y
1,2 : 2 1 2 1 3 1 5 2 9 0k
5 4 0k
Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c
2 1 3 5 9 0x y k x y
1,2 : 2 1 2 1 3 1 5 2 9 0k
5 4 0k
4 554
k
k
Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c
2 1 3 5 9 0x y k x y
1,2 : 2 1 2 1 3 1 5 2 9 0k
5 4 0k
4 554
k
k
52 1 3 5 9 04
x y x y
Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c
2 1 3 5 9 0x y k x y
1,2 : 2 1 2 1 3 1 5 2 9 0k
5 4 0k
4 554
k
k
52 1 3 5 9 04
x y x y
8 4 4 15 25 45 0x y x y
Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c
2 1 3 5 9 0x y k x y
1,2 : 2 1 2 1 3 1 5 2 9 0k
5 4 0k
4 554
k
k
52 1 3 5 9 04
x y x y
8 4 4 15 25 45 0x y x y
7 21 49 0x y
Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c
2 1 3 5 9 0x y k x y
1,2 : 2 1 2 1 3 1 5 2 9 0k
5 4 0k
4 554
k
k
52 1 3 5 9 04
x y x y
8 4 4 15 25 45 0x y x y
7 21 49 0x y 3 7 0x y
Alternatively 1 1 1 2 2 2 0a x b y c k a x b y c
2 1 3 5 9 0x y k x y
1,2 : 2 1 2 1 3 1 5 2 9 0k
5 4 0k
4 554
k
k
52 1 3 5 9 04
x y x y
8 4 4 15 25 45 0x y x y
7 21 49 0x y 3 7 0x y
Exercise 5F; 2b, 3b, 6b(i), 7ab (i, iii), 9, 10, 13*
Exercise 5G; 2 to 14 evens, 15*