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

}

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step-by-step explanation:

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