SOLUTION: find the distance between P(7,-4) and the line with equation x-3y+5=0.round to the nearest tenth

Question 216692: find the distance between P(7,-4) and the line with equation x-3y+5=0.round to the nearest tenth
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
find the distance between P(7,-4) and the line with equation x-3y+5=0.
round to the nearest tenth
:
Find the slope of the given equation
x - 3y + 5 = 0
-3y = -x - 5
Multiply eq by -1 to get rid of all those negatives
3y = x + 5
y = x +
:
The slope: m1 =
Find the slope of a line perpendicular (m2) to this equation
m1 * m2 = -1; the relationship of slopes of perpendicular lines
m2 = -1
m2 = -1*3
m2 = -3
:
Find the equation of the perpendicular line that passes thru P(7,-4)
Use the point/slope formula y - y1 = m(x - x1)
y -(-4) = -3(x - 7)
y + 4 = -3x + 21
y = -3x + 21 - 4
y = -3x + 17 is the equation of the perpendicular line
:
Find the value of x common to both equations
x + = -3x + 17
multiply both sides by 3
x + 5 = -9x + 51
x + 9x = 51 - 5
10x = 46
x =
x = 4.6
:
Find the value for y:
y = -3(4.6) + 17
y = -13.8 + 17
y = +3.2
:
Find the distance from points x1 = 7, y1 =-4 and x2 = 4.6, y2 =3.2
The distance formula d =
Using our point values
d =
d =
d =
d =
d = 7.589 ~ 7.6 dist between P(7,-4) and Eq x - 3y + 5 = 0.

RELATED QUESTIONS
find the distance between the points (4,4) and (-7- -7) round to the nearest... (answered by swincher4391)

find the distance between the points. Round your answer to the nearest tenth A(5,... (answered by jim_thompson5910)

find the distance between points P(1, 2) and Q(4, 8) to the nearest tenth (answered by Fombitz)

Find the distance between the points R (0, 5) and S (12, 3). Round your answer to the... (answered by MathLover1,josmiceli)

(-7,-8) and (1,7) find the distance between the given points. Round to the nearest tenth, (answered by josgarithmetic)

Use the Distance Formula to find the distance, to the nearest tenth, between K(-7,-4) and (answered by josgarithmetic)

find the distance between (-3,1) and (-1,6) . If necessary, round to the nearest... (answered by Earlsdon)

Find the distance between R(-1,1) and s(-4,-5) to the nearest... (answered by jim_thompson5910,Mr.Math)

Find the distance between points (3, 5) and (4, 6) to the nearest tenth. (answered by Alan3354)