A line with slope -3/4 passes through the point (5/3 -5/4) what is the distance between this line and the point (1, 1/2)?

Aeyang asked Jul 24, 2023

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Aeyang asked Jul 24, 2023

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14 votes

Answer:

Explanation:

The equation of the line is

$y+(5)/(4)=-(3)/(4)\left(x-(5)/(3) \right) \\ \\ y+(5)/(4)=-(3)/(4)x+(5)/(4) \\ \\ y=-(3)/(4)x \\ \\ 3x+4y=0$

Using the perpendicular distance formula,

d=(|(3)(1)+(4)(1/2)+0|)/(√(3^2+4^2))=1

Vivek Mohan answered Jul 30, 2023

3.0k points

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