Mathematics

Running head: MATHEMATICS 1
Mathematics
Name
Institution

MATHEMATICS 2
Question 1
Part a
A ( 3,14 ) , B ( 7,26 ) ,∧C(9,32)
AB= ( 7−3 , 26−14 ) = ( 4 , 12 ) =4(1,3)
BC= ( 9−7 , 32−26 ) = ( 2 , 6 ) =2(1,3)
Which implies that AB=2 BC. Since AB is a multiple of BC, the points lie on a straight.
Part b
Equation of AE
A ( 3,14 ) ∧E(5,0)
Gradient= 0−14
5−3 =−14
2 =−7
Let the line pass through point A and an arbitrary point with coordinates (x , y ).
Gradient= y−14
x −3 =−7
y−14=−7 ( x−3)
y=−7 x +21+14=−7 x +35
y=−7 x +35
Equation of AF
A ( 3,14 )∧F(14,0)

MATHEMATICS 3
Gradient= 0−14
14−3 =−14
11
Let the line pass through point A and an arbitrary point with coordinates (x , y ).
Gradient= y−14
x −3 =−14
11
y−14=−14
11 ( x−3 ) =−14
11 x + 42
11
y=−14
11 x+ 42
11 +14
y=−14
11 x+ 196
11
Equation of BD
B (7,26 )∧D(0,0)
Gradient= 0−26
0−7 =−26
−7 = 26
7
Let the line pass through point D and an arbitrary point with coordinates (x , y ).
Gradient= y−0
x−0 = 26
7
y= 26
7 x
Equation of BF
B ( 7,26 ) ∧F (14,0)
Gradient= 0−26
14−7 =−26
7

MATHEMATICS 4
Let the line pass through point B and an arbitrary point with coordinates (x , y ).
Gradient= y−26
x−7 =−26
7
y−26=−26
7 ( x−7)
y=−26
7 x+ 26+26=−26
7 x+ 52
y=−26
7 x+52
Equation of CD
C ( 9,32 ) ∧D(0,0)
Gradient= 0−32
0−9 =−32
−9 = 32
9
Let the line pass through point D and an arbitrary point with coordinates (x , y ).
Gradient= y−0
x−0 = 32
9
y= 32
9 x
Equation of CE
C (9,32)∧E(5,0)
Gradient= 0−32
5−9 =−32
−4 =8
Let the line pass through point E and an arbitrary point with coordinates (x , y ).