The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB.
What is the distance from P=(2,−2) to the line through the points A=(−5,−4) and B=(3,−1)
What is the distance from P=(2,−2) to the line through the points A=(−5,−4) and B=(3,−1)
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What is the distance from P=(2,−2) to the line through the points A=(−5,−4) and B=(3,−1)
First identify the equation of the line formed by A to B: y₁= 3x/8+ + -17/8
The line that is perpendicular to y1 and passing through (2, -2): y₂= -8x/3 + 10/3
To find intersection point of these two lines solve y₁= y₂
Or 3x/8+ + -17/8 = -8x/3 + 10/3
x = 131/73, so y = -106/73 \\ you should check these results in the original equations
Now find the distance from(2, -2) to(131/73, -106/73)
That distance = √[(2 ‒ 131/73)² + (-2 ‒ -106/73)²] = I will let you do this final step
First identify the equation of the line formed by A to B: y₁= 3x/8+ + -17/8
The line that is perpendicular to y1 and passing through (2, -2): y₂= -8x/3 + 10/3
To find intersection point of these two lines solve y₁= y₂
Or 3x/8+ + -17/8 = -8x/3 + 10/3
x = 131/73, so y = -106/73 \\ you should check these results in the original equations
Now find the distance from(2, -2) to(131/73, -106/73)
That distance = √[(2 ‒ 131/73)² + (-2 ‒ -106/73)²] = I will let you do this final step