What is the distance between the points (0, 5) and (3, 9)?

Expert Answers
hala718 eNotes educator| Certified Educator

Let the points be A= ( 0,5) and B = (3,9)

To find the distance between the points A and B,  we will use the distance formula as follows:

The distance Between A and B  is given by:

D ( AB) = sqrt[( xB-xA)^2 + ( yB-yA)^2].

Let us substitute with the coordinates of A and B.

==> D ( AB) = sqrt[ ( 3-0)^2 + ( 9-5)^2]

==> D(AB) = sqrt( 3^2 + 4^2)

==> D(AB) = sqrt(9+ 16).

==> D(AB) = sqrt25.

==> D(AB) = 5

Then, the distance between A and B is 5 units.

giorgiana1976 | Student

To determine the distance between 2 given points in the rectangular plane, we'll apply the Pythagorean theorem in the right angle triangle formed by the projections of the given points.

We'll note the points as A(0,5) and B(3,9).

The right angle triangle is ACB, where <C = 90 degrees and AB is the hypothenuse.

We'll calculate the cathetus AC:

AC = xA - xC

AC = 0 - 3

AC = -3

BC = yB - yC

BC = 9 - 5

BC = 4

The hypothenuse AB:

AB^2 = AC^2 + BC^2

AB^2 = (-3)^2 + 4^2

AB^2 = 9 + 16

AB^2 = 25

AB = sqrt 25

AB = 5 units

We'll keep just the positive value, since AB represents a distance.

neela | Student

The distance d between the two ponts (x1,y1) and (x2,y2) is given by:

 d = sqrt{(x2-x1)^2+(y2-y1)^2}.

So the distance between (0,5) and (3,9) is given by:

d = {(3-0)^2 +(9 - 5)^2} = sqrt{3 + 4^2}.

d = sqrt{9+16} = sqrt25

d = 5.

Therefore the distance between (0,5) and (3,9) is 5.