Question 223775
x-2y=12
-2y=12-x
y=x/2 -6
the y intercept where x=0 is y=-6
x/2 -6=0
x/2=6
x=12
The x intercept where y=0 is x=12
.
a^2+b^2=c^2
6^2+12^2=c^2
36+144=180
sqrt(180)
=sqrt(36*5)
=6sqrt(5) length of AB
3sqrt(5) midpoint of AB
.
tan=opp/adj=12/6=2 angle opposite line from midpoint to origin.
tan^-1(2)=63.42... deg
.
Law of cosines:
a^2=b^2+c^2-2bc cos(a)
a^2=6^2+(3sqrt(5))^2-2*6*3sqrt(5)*cos(63.42...)
a^2=36+45-36sqrt(5)*cos A
=45
sqrt(45)
=sqrt(9*5)
=3sqrt(5)
.
Ed