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Find in simplest radical form, the length of the line segment with endpoints whose coordinates are (-1,4) and (3,-2)?

Verified Answer :

Panoyin

\(d = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}} \\d = \sqrt{(3 - (-1))^{2} + (-2 - 4)^{2}} \\d = \sqrt{(3 + 1)^{2} + (-6)^{2}} \\d = \sqrt{(4)^{2} + 36} \\d = \sqrt{16 + 36} \\d = \sqrt{52} \\d = 2\sqrt{13}\)

Louli

Answer:

The distance is \(2\sqrt{13}\) units


Explanation:

The distance between two points can be calculated using the following rule:

distance = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\)


The given points are:

(-1,4) representing (x₁,y₁)

(3,-2) representing (x₂,y₂)


Substitute in the formula with the givens to get the distance as follows:

distance = \(\sqrt{(3--1)^2+(-2-4)^2} = 2\sqrt{13}\) units


Hope this helps :)

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