SOLUTION: find the distance from (2,1) to the line defined by y=-2x-5. Express as a radical or a number rounded to the nearest hundredth

Question 178276: find the distance from (2,1) to the line defined by y=-2x-5. Express as a radical or a number rounded to the nearest hundredth
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
find the distance from (2,1) to the line defined by y=-2x-5. Express as a radical or a number rounded to the nearest hundredth
-----------------------------
Do it like this one.
------------------------
find the distance from (6,5) to the line defined by y=-2x-8. express as radical or a number rounded to the nearest hundredth
-------------------------
Find the eqn of the line thru (6,5) perpendicular to y=-2x-8.
All lines perpendicular to it have a slope, m, that's the inverse negative.
y = -2x - 8 is in slope-intercept form, and its slope is -2, so we will find a line thru (6,5) with a slope of +1/2.
y - y1 = m*(x - x1) where (x1,y1) is (6,5)
y - 5 = (1/2)*(x - 6)
2y - 10 = x - 6
2y = x + 4
----------------
Solve the pair of eqns by subbing y into 2y = x + 4
2y = x + 4
2*(-2x-8) = x+4
-4x-16 = x+4
5x = -20
x = -4
-------------
y = -2x-8 = -2*(-4)-8
y = 0
The lines intersect at (-4,0)
-----------------
Now find the distance from (6,5) to (-4,0)
s = sqrt((diff in y)^2 + (diff in x)^2)
s = sqrt((0-5)^2 + (-4-6)^2)
s = sqrt(25+100) = sqrt(125)
distance =~11.2 units
RELATED QUESTIONS
Find the distance from (6,-3)to the line defined by y= 2x-5. Express as a radical or a... (answered by Alan3354,Fombitz,Edwin McCravy)

Find the distance from(2,-7) to the line defined by y=2x-6. Express as a radical or a... (answered by rfer)

From the distance from (-4,-1) to the line defined by y=-2x+1. Express as a radical or a... (answered by Fombitz)

find the distance from(-6,6) to the line defined by y=2x+3 express as a radical or a... (answered by josgarithmetic,ikleyn)

find the distance from (6,5) to the line defined by y=-2x-8. express as radical or a... (answered by Alan3354)

Find the distance form (4,-5) to the line defined by y=-2x+8. Express as a radical or a... (answered by Alan3354)

find the distance from (-6,-3) to the line defined by 3x+5. express as a radical or a... (answered by Alan3354)

Can someone explain how to find the distance from (-5,6) to the line defined by y=-5x+7.... (answered by solver91311)

find the distance from (-6,-5) to the line defined by y = -2x - 2. Express as a radical... (answered by ewatrrr,Edwin McCravy,josgarithmetic)