SOLUTION: What is the distance between point (9,18) and the line 30x-15y=75

Question 1066041: What is the distance between point (9,18) and the line 30x-15y=75
Found 4 solutions by josgarithmetic, stanbon, MathTherapy, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
What is the equation of the line through point (9,18) having slope ? Where does that line intersect with ? What is the distance between the two points (use the Distance Formula).
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
What is the distance between point (9,18) and the line 30x-15y=75
Slope of given line:: m = 30/15 = 2
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Slope of perdicular line thru (9,18)
m = -1/2
Form:: y = mx+b
18 = (-1/2)9 + b
b = 22.5
Equation:: y = (-1/2)x+22.5
----
Find intersection of the two lines::
y = 2x -5
y = (-1/2)x+22.5
-----
2x-5 = (-1/2)x+22.5
2.5x = 27.5
x = 11
y = 2x-5 = 22-5 = 17
----
Distance from (9,18) to (11,17)
d = sqrt[(11-5)^2+(18-17)^2] = sqrt[37]
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Cheers,
Stan H.
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Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
What is the distance between point (9,18) and the line 30x-15y=75

The 2 lines intersect at: (11, 17)
Distance from point (9, 18) to (11, 17), or
d, or PERPENDICULAR distance between (9, 18) and (11, 17) =
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
Let the straight line in a coordinate plane is defined in terms of its linear equation

,                       (1)

where a, b and c are real numbers, and let P = P(,) is the point in the coordinate plane
with the coordinates , . Then the distance from the point P to the straight line (1) is equal to

= .                (2)

See the lesson
    - The distance from a point to a straight line in a coordinate plane
in this site.

By applying this formula, you get

d = = = = = 2.236 (approximately).

It is very useful to know this formula and to apply it properly and correctly when it is needed.
It will save you a lot of efforts and time.

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