SOLUTION: find the distance from (-6,-5) to the line defined by y = -2x - 2. Express as a radical or number rounded to the nearest hundredth, is the question. can you tell me how to work thi

Algebra ->  Length-and-distance -> SOLUTION: find the distance from (-6,-5) to the line defined by y = -2x - 2. Express as a radical or number rounded to the nearest hundredth, is the question. can you tell me how to work thi      Log On


   

Question 859827: find the distance from (-6,-5) to the line defined by y = -2x - 2. Express as a radical or number rounded to the nearest hundredth, is the question. can you tell me how to work this out to get the right answer and help me solve it asap please and thank you.
Found 3 solutions by ewatrrr, Edwin McCravy, josgarithmetic:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

y+=green%28+-2%29x+-+2 Green, m = -2

***Using point-slope form, y+-+y%5B1%5D+=+m%28x+-+x%5B1%5D%29 P(-6,-5), m = 1/2

 y +5 = (1/2)(x+6)

    y = .5x - 2

Intersect at P(0,-2)

(0,-2)

(-6,-5)  D = sqrt(3^2 + 6^2) = sqrt(45) = 3sqrt(5)

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
The perpendicular distance from the point 

(x1,y1)

to the line 

Ax + By + C = 0 is

d = abs%28%28Ax%5B1%5D%2BBy%5B1%5D%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29
 
In your case, (x1,y1) = (-6,-5)

And the line is

 y = -2x - 2.

but we must first get it in the form

Ax + By + C = 0

 y = -2x - 2

2x + y + 2 = 0

So A = 2, B = 1, C = 2, x1 = -6, y1 = -5.

d = abs%28%28Ax%5B1%5D%2BBy%5B1%5D%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29


d = abs%28%282%28-6%29%2B1%28-5%29%2B2%29%2Fsqrt%282%5E2%2B1%5E2%29%29

d = abs%28%28-12-5%2B2%29%2Fsqrt%284%2B1%29%29

d = abs%28%28-15%29%2Fsqrt%285%29%29

d = %2815%29%2Fsqrt%285%29

Rationalize the denominator:

d = %2815%2Fsqrt%285%29%29%28sqrt%285%29%2Fsqrt%285%29%29

d = %2815sqrt%285%29%29%2F5

d = 3sqrt%285%29

Edwin

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The question would be the same as, find the equation of the line perpendicular to y=-2x-2 and containing the point (-6,-5); where do these lines intersect; and then use distance formula to find the distance from the intersection point to (-6,-5).

y=%281%2F2%29x%2Bb contains (-6,-5).
b=y-%281%2F2%29x
b=-6-%281%2F2%29%28-5%29
b=-6%2B5%2F2
b=-12%2F2%2B5%2F2
b=-7%2F2
y=%281%2F2%29x-7%2F2

What is the intersection point of y=-2x-2 and y=(1/2)x-7/2 ?
-2x-2=%281%2F2%29x-7%2F2
-4x-4=x-7
-5x-4=-7
-5x=4-7=3
x=-3%2F5
-
y=-2%28-3%2F5%29-2=6%2F5-2
y=6%2F5-10%2F5
y=-4%2F5
-
Intersection point is (-3/5, -4/5).

Distance from (-6,-5) to y=-2x-2 is:
highlight%28sqrt%28%28-6-%28-3%2F5%29%29%5E2%2B%28-5-%28-4%2F5%29%29%5E2%29%29