Question

10. Find the length of the
perpendicular from the point
5,4 on the straight line 2x+3y=4.
​

Answer 1

Answer :

18/√13

Note :

The perpendicular distance from the point (x1 , y2) and the straight line ax + by + c = 0 is given by : d = | ax1 + by1 + c | / √(a² + b²)

Solution :

Here ,

The given straight line is ;

2x + 3y = 4

The given straight line in its general form will be written as : 2x + 3y + (-4) = 0 .

Now ,

Comparing the above equation with the general equation of straight line , we have ;

a = 2

b = 3

c = -4

Now ,

=> √(a² + b²) = √(2² + 3²)

=> √(a² + b²) = √(4 + 9)

=> √(a² + b²) = √13

Now ,

The perpendicular distance of the point (x1 , y1) = (5 , 4) and the straight line 2x + 3y + (-4) = 0 will be given as ;

=> d = | ax1 + by1 + c | / √(a² + b²)

=> d = | 2•5 + 3•4 + (-4) | / √13

=> d = | 10 + 12 - 4 | / √13

=> d = | 18 | / √13

=> d = 18/√13

Hence ,

Required distance is 18/√13 .