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If A = (-1, -3) and B = (11, -8), what is the length of AB ?
A.12 units
B.13 units
C.11 units
D.14 units

Respuesta :

Apocrophon
For this problem, you need to know the distance formula, as that'll give you the length of the line segment.

[tex]distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\ where\ you\ have\ points\ (x_{1},y_{1})\ and\ (x_{2},y_{2}).[/tex]

Using points A and B, the formula becomes:
[tex]A=(x_{1},y_{1})=(-1,-3)\\B=(x_{2},y_{2})=(11,-8)\\x_{1}=-1\\x_{2}=11\\y_{1}=-3\\y_{2}=-8\\\\distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\length\ of\ AB=\sqrt{(11-(-1))^{2}+((-8)-(-3))^{2}}\\\\ length\ of\ AB=\sqrt{(11+1)^{2}+(3-8)^{2}}\\\\length\ of\ AB=\sqrt{(12)^{2}+(-5)^{2}}\\\\length\ of\ AB=\sqrt{144+25}\\\\length\ of\ AB=\sqrt{169}\\\\length\ of\ AB=\pm 13[/tex]

Length cannot be negative, so the length of AB is 13.

The length AB is 13 units.

Distance

It is a length that is measured during moving is called distance.

Distance formula between two points

[tex]\rm Distance = \sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }\\[/tex]

Given

A (-1, -3)

B (11, -8)

To find

The length AB.

How to find the length AB?

Length AB is given by,

[tex]\rm Distance = \sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }\\[/tex]

[tex]\rm (x_{1} ,y_{1} )[/tex] is (-1, -3) and [tex]\rm (x_{2} ,y_{2} )[/tex] is (11, -8) then

[tex]\rm Distance = \sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }\\\\\rm Distance = \sqrt{(11-(-1) )^{2} +(-8 -(-3))^{2} }\\\\\rm Distance = \sqrt{(12 )^{2} +(5 )^{2} }\\\\\rm Distance = \sqrt{144+25 }\\\\\rm Distance = \sqrt{169 }\\\\\rm Distance =13[/tex]

Thus the length AB is 13 units.

More about the distance link is given below.

https://brainly.com/question/989117

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