Answer:
Explanation:
P will be the point of intersection between the given line and a perpendicular line through the given point.
The given line has a slope (x-coefficient) of 3, so the perpendicular line will have a slope that is the negative reciprocal of that: -1/3. In point-slope form, the line through the given point is then ...
... y = (-1/3)(x -30)
The point of intersection can be found by setting the y-values equal.
... 3x = y = (-1/3)(x - 30)
... 9x = -x +30 . . . . . . . . . . multiply by 3, eliminate parentheses
... 10x = 30 . . . . . . . . . . . . add x
... x = 3 . . . . . . . . . . . . . . . . divide by 10
Now, either equation can be used to find y. It is convenient to use the simpler equation:
... y = 3x = 3·3 = 9
So, the point of intersection is ...
... P = (3, 9)
_____
The distance between this point and the given point can be found using the Pythagorean theorem.
- The x-distance between the points is 30 -3 = 27.
- The y-distance between the points is 9 - 0 = 9.
The straight-line distance between the points is ...
... d = √(27² +9²) = 9√(3² +1²) = 9√10
