SOLUTION: Given the line defined by the equation x=2-5t y=3+6t a.does the point (8,-3)lie on the line ? b.determine the scalar equation of the line c.find the shortest distance from

Question 1153599: Given the line defined by the equation
x=2-5t
y=3+6t
a.does the point (8,-3)lie on the line ?
b.determine the scalar equation of the line
c.find the shortest distance from the line to point (1,3)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Given the line defined by the equation
x=2-5t
y=3+6t
------------
x=2-5t --> t = (2-x)/5
---
y=3+6t
Sub for t
y = 3 + (12-6x)/5
5y = 15 + 12-6x
6x + 5y = 27
================
a.does the point (8,-3)lie on the line ?
6*8 + 5*-3 =? 27
No.
--------------
b.determine the scalar equation of the line
6x + 5y = 27
--------------
c.find the shortest distance from the line to point (1,3)
6x + 5y - 27 = 0
d = |6*1 + 5*3 - 27|/sqrt(6^2 + 5^2) = 6/sqrt(61) units.
d = 6sqrt(61)/61 units
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