Question 570227
Calculate the distance from point (-2,3) to the line y=x+1
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The distance from a point to a line is the shortest distance, which is along the line perpendicular to the given line.
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The slope, m of y = x + 1 is 1.
The slope of lines perpendicular is the neg inverse, = -1
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Find the eqn of the line thru the point with a slope of -1.
y = mx + b
3 = -1*(-2) + b
b = 1
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The line perpendicular thru the point is
y = -x + 1
Find the intersection of the 2 lines.
y = x + 1
y =-x + 1
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2y = 2
y = 1
x = 0
The point (0,1) is the intersection.
Find the distance from (0,1) to (-2,3)
{{{d = sqrt(diffy^2 + diffx^2) = sqrt(4 + 4)}}}
{{{d = 2sqrt(2)}}}