Question

What is the distance from point (– 1, 3) to the line 3x – 4y = 10?​

Answer 1

5 units

Explanation:

The distance from a point (m, n ) to the line Ax + By + C = 0 is given by

d =
`(|Am+Bn+C|)/(√(A^2+B^2) )`

For the point (- 1, 3 ) , with m = - 1 and n = 3

3x - 4y = 10 ( subtract 10 from both sides )

3x - 4y - 10 = 0

with A = 3 , B = - 4 , C = - 10

d =
`(|3(-1)+(-4)3-10|)/(√(3^2+(-4)^2) )`

=
`(|-3-12-10|)/(9+16)`

=
`(|-25|)/(√(25) )`

=
`(25)/(5)`

= 5