What is the perpendicular distance of the point (3, 8) from the line x - y + 8 = 0

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The perpendicular distance of the point (3, 8) from the line x - y + 8 = 0 has to be determined.

An easy way to do this is to use the formula for the perpendicular distance of a point `(x_1, y_1)` from the line ax + by + c = 0 which is given by `|a*x_1 + b*y_1 + c|/sqrt(a^2 + b^2)`

Substituting the values in the problem:

`D = |1*3 - 1*8 + 8|/sqrt(1 + 1)`

=> `3/sqrt 2`

The perpendicular distance of the point (3, 8) from the line x - y + 8 = 0 is `3/sqrt 2`

blujayregine's profile pic

blujayregine | Student, College Freshman | (Level 1) eNoter

Posted on

The equation of the distance of a point to a line is d= `(Ax+By+C)/(+-sqrt(A^2+B^2))`

` `

(3,8) as (x,y) and from the equation x-y+8=0 A= 1 ; B= -1 ; C= 8

substitute this to the equation:

d= `(1(3)+(-1)(8)+8)/(+-sqrt(1^2+(-1)^2))`

the answer is `(3sqrt(2))/(2)`

 

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