d: (13,-1)
step-by-step explanation:
we know the starting point is (1,5)
the ending point is (x,y) (cristians house)
the total distance is 6 units (5: 1)
the fast food restaurant is at (11,0) and is 5/6ths of the way from the starting point to the ending point
ending minus starting point * 5/6 is how far they went
(x-1) *5/6, (y-5) * 5/6
we then need to add the starting point to determine the location
5/6(x-1) + 1, (y-5) * 5/6 + 5
this equals the fast food location of 11,0
setting the x locations equal
5/6 (x-1) +1 =11
subtracting 1 from each side
5/6 (x-1) +1-1 =11-1
5/6(x-1) =10
multiplying by 6/5 on each side
6/5*5/6(x-1) = 10*6/5
x-1 =12
add 1 to each side
x-1+1 =12+1
x=13
do the same for the y coordinate
(y-5) * 5/6 + 5 =0
subtract 5 from each side
(y-5) * 5/6 + 5-5 =0-5
5/6 (y-5) = -5
multiplying by 6/5 on each side
6/5*5/6 (y-5) = -5 *6/5
y-5 = -6
add 5 to each side
y-5+5 = -6+5
y=-1
the ending point , or the coordinates of cristians house is
(13,-1)