SOLUTION: Given (9, 4) and (x,- 8), find all x such that the distance between these two points is 13. Separate multiple answers with a comma,

Algebra ->  Coordinate-system -> SOLUTION: Given (9, 4) and (x,- 8), find all x such that the distance between these two points is 13. Separate multiple answers with a comma,      Log On


   

Question 1197077: Given (9, 4) and (x,- 8), find all x such that the distance between these two points is 13. Separate multiple answers with a comma,
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The distance formula is:

d=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29

given:
(x%5B1%5D, y%5B1%5D) =(9, 4)
(x%5B2%5D, y%5B2%5D) = (x,-+8)
d=13

plug in distance formula:

13=sqrt%28%28x-9%29%5E2%2B%28-8-4%29%5E2%29
13=sqrt%28x%5E2+-+18x+%2B+225%29...........square both sides
13%5E2=x%5E2+-+18x+%2B+225
169=x%5E2+-+18x+%2B+225
0=x%5E2+-+18x+%2B+225-169
0=x%5E2+-+18x+%2B+56.........factor
0=x%5E2+-4x-+14x+%2B+56
0=%28x%5E2+-4x%29-+%2814x+-+56%29
0=x%28x+-4%29-14+%28x+-+4%29
+%28x+-+14%29+%28x+-+4%29=0

solutions:

if +%28x+-+14%29+=0 =>x=14
if +%28x+-+4%29+=0 =>x=4



the point (x,-+8) could be:
(14,-+8)
or
(4,-+8)

answer: 4, 14

check the answer:

(9, 4) and (14,-+8)
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%2814-%289%29%29%5E2%29%2B%28%28-8-%284%29%29%5E2%29%29
sqrt%285%5E2%2B-12%5E2%29 The distance is 13.



and

(9, 4) and (4,-+8)
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%284-%289%29%29%5E2%29%2B%28%28-8-%284%29%29%5E2%29%29
sqrt%28-5%5E2%2B-12%5E2%29 The distance is 13.