SOLUTION: What is the distance between the points (2, -4) and (-3, 5)?

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Question 824296: What is the distance between the points (2, -4) and (-3, 5)?

Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (2, -4), we can say (x1, y1) = (2, -4)
So x%5B1%5D+=+2, y%5B1%5D+=+-4


Since the second point is (-3, 5), we can also say (x2, y2) = (-3, 5)
So x%5B2%5D+=+-3, y%5B2%5D+=+5


Put this all together to get: x%5B1%5D+=+2, y%5B1%5D+=+-4, x%5B2%5D+=+-3, and y%5B2%5D+=+5

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Now use the distance formula to find the distance between the two points (2, -4) and (-3, 5)



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


d+=+sqrt%28%282+-+%28-3%29%29%5E2+%2B+%28-4+-+5%29%5E2%29 Plug in x%5B1%5D+=+2, y%5B1%5D+=+-4, x%5B2%5D+=+-3, and y%5B2%5D+=+5


d+=+sqrt%28%282+%2B+3%29%5E2+%2B+%28-4+-+5%29%5E2%29


d+=+sqrt%28%285%29%5E2+%2B+%28-9%29%5E2%29


d+=+sqrt%2825+%2B+81%29


d+=+sqrt%28106%29


d+=+10.295630140987

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Answer:


The distance between the two points (2, -4) and (-3, 5) is exactly sqrt%28106%29 units


The approximate distance between the two points is about 10.295630140987 units



So again,


Exact Distance: sqrt%28106%29 units


Approximate Distance: 10.295630140987 units



Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the general formula which is based on
the pythagorean theorem:
-----------------------
If the given points are:
( x1, y1 ) and ( x2, y2 )
then
Distance between the points =
square root of [ ( x2 - x1 )^2 + ( y2 - y1 )^2 ]
---------------------------------------
For your problem:
( x1, y1 ) = ( 2,-4 )
( x2, y2 ) = ( -3,5 )
Distance = +sqrt%28+%28+-3+-2+%29%5E2+%2B+%28+5+-%28-4%29+%29%5E2+%29+
Distance = +sqrt%28+%28+-5+%29%5E2+%2B++9%5E2+%29+
Distance = +sqrt%28+25+%2B+81+%29+
Distance = +sqrt%28+106+%29+
Distance = 10.296