CBSE Class 11-science Answered
members planner to go A family of 4for Goa by train during summer for adventures. On the day of Journey all the auto/taxi drivers were on strike due to price hike of petrol. So the family couldn’t get any transport to railway station. Now family is standing at the crossing of two straight roads represented by equations 2x–3y– 4=0 and 3x–4y–5=0, want to reach the path whose equation is 6x–7y+8=0 in least time. Find the equation of path that they should follow any why?
Asked by amogha4920 | 22 Mar, 2019, 10:43: AM
Expert Answer
At first, let us get the intersection point, where family is standing by solving the following equations
2x - 3y = 4 .............................(1)
3x - 4y = 5 .............................(2)
eqn.(1) × 3 gives, 6x - 9y = 12 ......................(3)
eqn.(2) × 2 gives, 6x - 8y = 10 ......................(4)
By subtracting eqn.(4) from eqn.(3), we get y = -2 ; by substituting y = -2 in eqn.(1) and solve for x, we get x = -1
hence Standing point of family (-1, -2)
Let us find the intersection of paths represented by following lines
2x - 3y = 4 ..........................(5)
6x - 7y = -8 .........................(6)
eqn.(5)×3 gives, 6x -9y = 12 ...............(7)
By subtracting eqn.(6) from eqn.(7), we get y = -10 ; by substituting y = -10 in eqn.(5), we get x = -13
Hence intersection point of paths represented by equations 2x-3y-4 = 0 and 6x-7y+8 = 0 is (-13, -10 )
Let us find the intersection of paths represented by following lines
3x - 4y = 5 ..........................(8)
6x - 7y = -8 .........................(9)
eqn.(8)×2 gives, 6x -8y = 10 ...............(10)
By subtracting eqn.(9) from eqn.(7), we get y = -18 ; by substituting y = -18 in eqn.(8), we get x = - 
Hence intersection point of paths represented by equations 3x-4y-5 = 0 and 6x-7y+8 = 0 is (-18, - )
)
Figure given above shows the three paths represented by the given equations. Family is standing at A (-1, -2).
Family need to reach the path represented by eqn. 6x-7y+8 =0 ( green line in figure).
To reach the path from A, family can go along AB or AC.
Since AB is shorter ditance in comparision with AC, the path AB is the correct path ( red line )
and this path is represented by line 2x-3y = 4
Answered by Thiyagarajan K | 22 Mar, 2019, 01:45: PM
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