find the distance between the points (5,7) and (7,5)? Justify your answer if they are equal?
Answers
Example 1
graph 2 points
Fill in the values: c = square root of [(9-3)^2+(7-2)^2]
c = square root of [6^2+5^2] = square root of 61
Example 2
It doesn't matter what order the points are in, because squaring removes any negatives:
graph 2 points
Fill in the values: c = square root of [(3-9)^2+(2-7)^2]
c = square root of [(-6)^2+(-5)^2] = square root of 61
Example 3
And here is another example with some negative coordinates ... it all still works:
graph 2 points
Fill in the values: c = square root of [(-3-7)^2+(5-(-1))^2]
c = square root of [(-10)^2+(6)^2] = square root of 136
(Note √136 can be further simplified to 2√34 if you want)
Try It Yourself
Drag the points:
d = √( (9.0−4.0)2 + (4.5−3.0)2 )
= √( (5.0)2 + (1.5)2 )
≈ 5.220CoordsGuidesResetEdit
✔✘© 2016 MathsIsFun.com v0.883
Three or More Dimensions
It works perfectly well in 3 (or more!) dimensions.
Square the difference for each axis, then sum them up and take the square root:
Distance = √[ (xA − xB)2 + (yA − yB)2 + (zA − zB)2 ]
distance between (9,2,7) and (4,8,10) in 3d
Example: the distance between the two points (8,2,6) and (3,5,7) is:
= √[ (8−3)2 + (2−5)2 + (6−7)2 ]
= √[ 52 + (−3)2 + (−1)2 ]
= √( 25 + 9 + 1 )
= √35
Which is about 5.9
Step-by-step explanation:
let the coordinate (5,7) be x
and coordinate (7,5) be y
(X1+x 2/2,y 1+y 2/2)
(5+7/2,7+5/2)
(12/2,12/2)
(6,6)