# Find the distance between the points (0,2) ( -1, -4) and between( 3,-4 ) ( -1, 3)

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The distance between (0, 2) and ( -1, -4).

We will use the distance formula to calculate.

We know that the distance formula is:

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

==> D = sqrt[ ( 0+1)^2 + ( 2+4)^2]

= sqrt( 1+ 36)

= sqrt(37)

**Then, the distance between the point ( 0,2) and the point (-1,-4) = sqrt(37) = 6.08 units ( approx.)**

The distance between ( 3, -4) and ( -1,3).

We will us the distance formula to calculate the distance.

D = sqrt[ ( 3+1)^2 + ( -4-3)^2]

= sqrt( 4^2 + 7^2)

= sqrt( 16 + 49)

= sqrt( 65) = 8.06

**Then, the distance between the point ( 3,-4) and the point ( -1,3) = sqrt(65) = 8.06 units ( approx.)**

The distance between 2 points in a rectangular plane could be found using Pythagorean theorem.

We'll note the distance between the first 2 points as d1. This distance represents the hypothenuse of the right angle triangle formed by the projections of the points.

d1^2 = (x2 - x1)^2 + (y2 - y1)^2

d1 = sqrt [(-1 - 0)^2 + (-4 - 2)^2]

d1 = sqrt (1 + 36)

**d1 = sqrt 37**

Now, we'll determine the distance between ( 3,-4 ) ( -1, 3), using Pythagorean theorem also.

We'll note this distance as d2.

d2^2 = (x4 - x3)^2 + (y4 - y3)^2

d2 = sqrt [(-1 - 3)^2 + (3 + 4)^2]

d2 = sqrt (16+49)

**d2 = sqrt 65**