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December 5, 2016
Posted by **Lily** on Friday, December 20, 2013 at 8:02pm.

I don't get the x+y=3 mean

- Math grade 9 -
**Damon**, Friday, December 20, 2013 at 8:40pmWell, it means the shortest distance, that along a perpendicular from the point to the line.

- Math grade 9 -
**Damon**, Friday, December 20, 2013 at 8:41pmslope of the line y = -x + 3 is -1

so

the slope of the perpendicular is -1/-1 = 1 - Math grade 9 -
**Damon**, Friday, December 20, 2013 at 8:43pmthen find the equation of that perpendicular through the given point

y = 1 x + b

goes through our point (5,6)

so

6 = 5 + b

b = 1

so the equation of our perpendicular is

y = x + 1 - Math grade 9 -
**Damon**, Friday, December 20, 2013 at 8:46pmNow where does that hit our original line?

y = -x + 3

y = x + 1

------------- add them

2 y = 4

y = 2

then x = 1

so at

(1,2)

NOW I have an easy problem that I bet you know how to do.

Find the distance from

(5,6) to (1,2) - Math grade 9 -
**Damon**, Friday, December 20, 2013 at 8:49pmd^2 = (1-5)^2 + (2-6)^2

d^2 = 16 + 16

d^2 = 2*4^2

d = 4 sqrt 2 - Math grade 9 -
**Reiny**, Friday, December 20, 2013 at 8:59pmIf (a,b) is a point not on the line

Ax + By + C = 0

then the shortest distance from the point to the line is

|aA + bB + C|/√(A^2+b^2)

shortest distance

= |5(1) + 6(1) -3|/√(1^2+1^2)

= 8/√2

which rationalizes to 4√2 - Math grade 9 -
**Damon**, Friday, December 20, 2013 at 9:03pmAre they supposed to know that Reiny ?

- Math grade 9 -
**Reiny**, Friday, December 20, 2013 at 9:21pmnot sure about grade 9, but I just checked an old grade 10 text from Ontario, and I used to teach it in 10

The proof followed your method using a general case. - Math grade 9 -
**Damon**, Saturday, December 21, 2013 at 2:23pmI think you had best learn that recipe Lily.