Alex wants to fence in an area for a dog park. he has plotted three sides of the fenced area at the points e (3,5), f(6,5), and g (9,1). he has 22 units of fencing. where could alex place point h so that he does not have to buy more fencing? a.(0,0) ,0) c(0,-3) d.(0,3)

(0,3)

step-by-step explanation:

so i'm going to compute the distance between (3,5) and (6,5), then the distance between (6,5) and (9,1). then i'm going to choose one of the choices given (x,y), and compute it's distance from (9,1) and then to (3,5). i'm going to add up all of these distances and see if is 22 or less. if it 22 or less we are okay.

the distance between (3,5) and (6,5) is a horizontal so all we have to do is count. that distance is 6-3 which is 3.

the distance between (6,5) and (9,1) is sqrt((9-6)^2+(5-1)^2)=sqrt(3^2+4^2)=sqrt(9+16)=sqrt(25)=5.

now i'm going to look at (0,0).   the distance between (9,1) and (0,0) is sqrt((9-0)^2+(9-0)^2)=sqrt(81+81)=sqrt(162)=approximately 12.7.

the last distance to include is the one from (0,0) to (3,5).   this distance is sqrt((3-0)^2+(5-0)^2)=sqrt(9+25)=sqrt(34)=approximately 5.8

3+5+12.7+5.8=26.5 which is too much.

we probably should have selected the point that seemed closer to the others like (0,3). let's try that.

so the only two new distances we have to compute is (0,3) to (9,1) and (0,3) to (3,5).

the distance from (0,3) to (9,1) is sqrt((9-0)^2+(3-1)^2)=sqrt(9^2+2^2)=sqrt(81+4)=sqrt(85)=approximately 9.2

the distance from (0,3) to (3,5) is sqrt((3-0)^2+(5-3)^2)=sqrt(3^2+2^2)=sqrt(9+4)=sqrt(13)=approximately 3.6

now 3+5+9.2+3.6 is 20.8.

the answer is (0,3).

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