Find the coordinates of the foot of the perpendicular from (6,8) the line through(1,5) and (9,3)

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Step-by-step explanation:

Let (a,b) be the coordinates of the foot of the perpendicular from the point (−1,3) to the line 3x−4y−16=0

Slope of the line joining (−1,3) and (a,b), is m

1

=

a+1

b−3

Slope of the line 3x−4y−16=0 or y=

4

3

x−4,m

2

=

4

3

Since these two lines are perpendicular,m

1

m

2

=−1

∴{

a+1

b−3

}⋅{

4

3

}=−1

⇒

4a+4

3b−9

=−1

⇒3b−9=4a−4

⇒4a+3b=5...(1)

Point(a,b) lies on line 3x−4y=16

∴3a−4b=16(2)

On solving equation (1) and (2) we obtain

a=

25

68

and b=−

25

49

Thus, the required coordinates of the foot of the perpendicular are {

25

68

,

25

49

}

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b