mr.schmidt drives to work on two straight road is 61/3 Miles long and the other road is 43/4 miles long.The road are at right angle s to each other.If a direct road were built between Me.Schmidt and Hawthorne, it would be 77/8 miles long How many miles would this road save Mr.Schmidt each trip
Answers
Answer:
A person standing at the junction (crossing) of two straight paths represented by the equations 2x−3y+4 = 0 and 3x+4y−5= 0 wants to reach the path whose equation is 6x−7y+8= 0 in the least time. Find equation of the path that he should follow.
Medium
Solution
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Given a person is standing at the junction of the below lines
2x−3y+4=0 ...(1)
3x+4y−5=0 ...(2)
Solving equation (1) and (2) ,we get
x=−
17
1
and y=
17
22
So, the person is standing at point (−
17
1
,
17
22
)
Given equation of path is
6x−7y+8=0 ...(3)
The person can reach this path in the least time if he walks along the perpendicular line to (3) from point (−
17
1
,
17
22
)
Slope of the line (3)=
7
6
∴ slope of the line perpendicular to line (3)=−
7
6
1
=−
6
7
The equation of the line passing through (−
17
1
,
17
22
) and having a slope of −
6
7
is given by
y−
17
22
=−
6
7
(x+
17
1
)
6(17y−22)=−7(17x+1)
102y−132=−119x−7
119x+102y=125
Hence, the path that person should follow is 119x+102y=125