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

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You need to use the distance formula to evaluate the length of segment AB such that:

`AB = sqrt((x_A - x_B)^2 + (y_B - y_A)^2)`

Identifying `A(x_A,y_A) = A(0,2)` and `B(x_B,y_B) = B(-1,-4)` yields:

`AB= sqrt((0 - (-1))^2 + (2 - (-4))^2)`

`AB = sqrt(1 + 36) => AB = sqrt37`

You need to use the distance formula to evaluate the length of segment CD such that:

`CD = sqrt((x_C - x_D)^2 + (y_C - y_D)^2)`

Identifying `C(x_C,y_C) = C(3,-4)` and `D(x_D,y_D) = D(-1,3)` yields:

`CD = sqrt((3 - (-1))^2 + (-4 - 3)^2)`

`CD = sqrt(16 + 49) => CD = sqrt 65`

**Hence, evaluating the lengths of the segments AB, CD, under the given conditions, yields **`AB = sqrt37, CD = sqrt 65.`

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