SOLUTION: Find the distance from point A(15,−21) to the line 5x+2y = 4. Round your answer to the nearest tenth.

Question 1146601: Find the distance from point A(15,−21) to the line 5x+2y = 4. Round your answer to the nearest tenth.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Find the distance from point to the given line
A(,),
.....first, write in slope intercept form

The slope of your GIVEN line is .
The slope of the line you want to find (perpendicular line) must have slope inverse reciprocal which is .
Line you want:
, using point-slope form

WHY? The two lines intersect at some point which you will find.
Then use Distance formula to find the length from the intersection point to point A(,).
You are first looking for the line perpendicular to the given one which contains point .

Now find intersection point of and . So, all you need is equal right sides.

go to , plug in and solve for

intersection point is at (,)

now use Distance formula to find the length from the intersection point to point A
A(,) = (,)
(,) = (,)

=> exact solution
=>to the nearest tenth

Answer by greenestamps(13216) (Show Source): You can put this solution on YOUR website!

The response from the other tutor shows a detailed solution to the problem.

You should be able to understand all the steps required for the solution; and you should be able to solve a similar problem by that method.

However, in practice, there is a concise formula for finding the (shortest) distance from a given point to a given line. When the equation of the line is in the form Ax+By+C=0, then the distance from a point (p,q) to the line is

In the required form, the equation in this problem is 5x+2y-4 = 0. Then the distance from (15,-21) to that line is

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