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how do i find the shorted distance between the point and the line

How Do I Find The Shorted Distance Between The Point And The Line class=

Sagot :

Answer:

5 units

Step-by-step explanation:

3x + 4y = 8

4y = -3x+8

y = -3/4+2

The shortest distance between a point and a line is the perpendicular line.

Slope of the perpendicular line: 4/3 and point (-3,-2)

b = -2-(4/3)(-3) = 2

Equation of the perpendicular line: y=4/3x+2

y is equal y

4/3x+2= -3/4x+2

4/3x +3/4x = 2-2

x = 0

Plug x=0 into one of the equations to find y

y = 4/3(0) + 2

y = 2

(0,2) and (-3,-2)

Distance = sqrt [(-3-0)^2 + (-2-2)^2]

Sqrt (-3)^2+ (-4)^2

Sqrt 25 = 5

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