Use the distance formula to find the distances between the given points:(5, 2) and (0,-4)

2 Answers | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

The problem provides the information that you need to use distance formula to evaluate the distance between the given points, such that:

`d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Identifying `(x_1,y_1) = (5,2)` and `(x_2,y_2) = (0,-4)` yields:

`d = sqrt((0 - 5)^2 + (- 4 - 2)^2)`

`d = sqrt(25 + 36) => d = sqrt 61`

Hence, evaluating the distance between the given points, using distance formula, yields `d = sqrt 61.`

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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(5, 2) and B(0,-4).

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 = 5 - 0

AC = 5

BC = yB - yC = 4 + 2 = 6

The hypothenuse AB:

AB^2 = AC^2 + BC^2

AB^2 = 5^2 + 6^2

AB^2 = 25 + 36

AB^2 = 61

AB = sqrt 61 units

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

We’ve answered 318,930 questions. We can answer yours, too.

Ask a question