SOLUTION: Hello out there,I really need some help with some tough problems,the first one is,Find the distance between the two points given.Round to the nearest tenth,if necessary,(1,1)and(3,

Algebra ->  Radicals -> SOLUTION: Hello out there,I really need some help with some tough problems,the first one is,Find the distance between the two points given.Round to the nearest tenth,if necessary,(1,1)and(3,      Log On


   

Question 112073: Hello out there,I really need some help with some tough problems,the first one is,Find the distance between the two points given.Round to the nearest tenth,if necessary,(1,1)and(3,2).The next one is,Find the distance between the two points given.Round to the nearest tenth,if necessary,(4,0)and(6,3).The third one is Find the distance between the two points given.Round to the nearest tenth,if necessary,(5,2)and(5,-2).And the last one is,Find the distance between the two points given.Round to the nearest tenth,if necessary,(1,3)and(1,5).Thanks to whoever can help.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1
Start with the given distance formula
d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 where is the first point and is the second point

d=sqrt%28%281-3%29%5E2%2B%281-2%29%5E2%29 Plug in x%5B1%5D=1, x%5B2%5D=3, y%5B1%5D=1, y%5B2%5D=2

d=sqrt%28%28-2%29%5E2%2B%28-1%29%5E2%29 Evaluate 1-3 to get -2. Evaluate 1-2 to get -1.

d=sqrt%284%2B1%29 Square each value

d=sqrt%285%29 Add

So the distance approximates to

d=2.23606797749979

which rounds to
2.2

So the distance between (1,1) and (3,2) is approximately 2.2 units



#2
Start with the given distance formula
d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 where is the first point and is the second point

d=sqrt%28%284-6%29%5E2%2B%280-3%29%5E2%29 Plug in x%5B1%5D=4, x%5B2%5D=6, y%5B1%5D=0, y%5B2%5D=3

d=sqrt%28%28-2%29%5E2%2B%28-3%29%5E2%29 Evaluate 4-6 to get -2. Evaluate 0-3 to get -3.

d=sqrt%284%2B9%29 Square each value

d=sqrt%2813%29 Add

So the distance approximates to

d=3.60555127546399

which rounds to
3.6

So the distance between (4,0) and (6,3) is approximately 3.6 units



#3
Start with the given distance formula
d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 where is the first point and is the second point

d=sqrt%28%285-5%29%5E2%2B%282--2%29%5E2%29 Plug in x%5B1%5D=5, x%5B2%5D=5, y%5B1%5D=2, y%5B2%5D=-2

d=sqrt%28%280%29%5E2%2B%284%29%5E2%29 Evaluate 5-5 to get 0. Evaluate 2--2 to get 4.

d=sqrt%280%2B16%29 Square each value

d=sqrt%2816%29 Add

d=4 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

So the distance between (5,2) and (5,-2) is 4 units



#4

Start with the given distance formula
d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 where is the first point and is the second point

d=sqrt%28%281-1%29%5E2%2B%283-5%29%5E2%29 Plug in x%5B1%5D=1, x%5B2%5D=1, y%5B1%5D=3, y%5B2%5D=5

d=sqrt%28%280%29%5E2%2B%28-2%29%5E2%29 Evaluate 1-1 to get 0. Evaluate 3-5 to get -2.

d=sqrt%280%2B4%29 Square each value

d=sqrt%284%29 Add

d=2 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

So the distance between (1,3) and (1,5) is 2 units

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the distance between the two points given.Round to the nearest tenth,if necessary,(1,1)and(3,2).
-----------------------------
Formula: d = sqrt[(1-3)^2 + (1-2)^2)] = sqrt[4 + 1] = sqrt(5)
================================
The next one is,Find the distance between the two points given.Round to the nearest tenth,if necessary,(4,0)and(6,3).
--------------------------------
d = sqrt[(4-6)^2 + (0-3)^2] = sqrt[4+9] = sqrt(13)
===========================
The third one is Find the distance between the two points given.Round to the nearest tenth,if necessary,(5,2)and(5,-2).
---------------------------
Follows the same pattern.
=======================
And the last one is,Find the distance between the two points given.Round to the nearest tenth,if necessary,(1,3)and(1,5).
------------------
Follows the same pattern.
========================
Cheers,
Stan H.