Respuesta :

JeanaShupp

Answer: [tex]XY=15.23[/tex]

Step-by-step explanation:

The distance between two points A(a,b) and B (c,d) is given by :-

[tex]AB=\sqrt{(c-a)^2+(d-b)^2}[/tex]

The given points : X(-9,2) Y(5,-4)

Then , the distance between two points X(-9,2) Y(5,-4) will be :-

[tex]XY=\sqrt{(5-(-9))^2+(-4-2)^2}\\\\\Rightarrow\ XY\sqrt{(5+9)^2+(-6)^2}\\\\\Rightarrow\ XY=\sqrt{(14)^2+(-6)^2}\\\\\Rightarrow\ XY=\sqrt{196+36}\\\\\Rightarrow\ XY=\sqrt{232}=15.2315462117\approx15.23[/tex]

Hence, [tex]XY=15.23[/tex]

akposevictor

The distance between X(-9,2) and Y(5,-4) is: 15.23 units.

Given:

[tex]X(-9,2) \\Y(5,-4)[/tex]

Apply the distance formula given as:

[tex]d = \sqrt{(y_2 - y_1)^2 - (x_2-x_1)^2 }[/tex]

Let,

[tex]X(-9,2) = (x_1,y_1)\\Y(5,-4) = (x_2,y_2)\\[/tex]

Plug in the values into the distance formula:

[tex]d = \sqrt{(-4 - 2)^2 + (5-(-9))^2 }\\= \sqrt{(-6)^2 + (14)^2 } = \sqrt{(36+196 }\\XY = \sqrt{232} \\XY = 15.23[/tex]

Therefore XY to the nearest hundredth is 15.23 units.

Learn more about distance between two points here:

https://brainly.com/question/17962414

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