find the distansce between each pair of points (1,5), (3,1)?

Question

express answers in simplest radical form and as decimal approximations rounded to the nearest hundredth if necessary

Answer 1

Use the distance formula... derived directly form the Pythagorean theorem...

sqr rt[(Xsub2 - Xsub1)^2 + (Ysub2 - Ysub1)^2]

(1,5) is (Xsub1 , Ysub1)
(3,1) is (Xsub2 , Ysub2)

so...

sqr rt[(3 - 1)^2 + (1 - 5)^2]
sqr rt[(2)^2 + (-4)^2]
sqr rt[4 + 16]
sqr rt (20) = 2*sqr rt(5) or approximately 4.47

Answer 2

The distance formula is:

d=√(x-x)² + (y-y)²

So this is how you use this formula:

d=√((1-3)² + (5-1)²) ----------So what I did was take the x coordinate from the first pair and the x from the second pari and substracted them...same for the y. If you used the numbers from the second pair first, makes sure you also use y from the second pair first....example: The way I did it up top can also be written...d=√((3-1)² + (1-5)²). You get the exact same answers in the end, but the signs are different before you take the square of it...that is way you are squaring the numbers because distance can't be negative....so go ahead and do the math....

d=√((1-3)² + (5-1)²)= √((-2)² + (4)²) =√(4+16)=√20

So your answer is √20, square root of 20.

Hope this helps!

Answer 3

The "x" distance is 2
The "y" distance is 4
The distance is sqrt(2^2+4^2)=sqrt(20)= 4.472
(doesn't everyone know sqrt(5) )??

Answer 4

[(1-X2)^2 + (Y1-Y2)^2]^1/2
[(1-3)^2 +(5-1)^2]= 2x5^1/2

Answer 5

d = √(x₂- x₁)² + (y₂- y₁)²

Use the distance formula.