Question

find the distance of the point (3,4) to the line 4x-3y+1=0

Answer 1

P(3,4)≡(x
1
​
,y
1
​
)

line ≡4x−3y−12=0

ax+by+c=0

the distance of the point from a line

=
∣
∣
∣
∣
​

a
2
+b
2

​

ax
1
​
+by
1
​
+c
​

∣
∣
∣
∣
​


=
∣
∣
∣
∣
​

4
2
+3
2

​

4×3+(−3)×4+(−12)
​

∣
∣
∣
∣
​


=∣
25
​

12−12−12
​
∣

=∣
5
−12
​
∣

=
5
12
​
units


Hope it is right