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MidnightShowers

[tex]\huge\underline\mathcal{\red{A}\purple{n}\orange{s}\blue{w}\green{e}\pink{r} -}[/tex]

  • Given - two points , say A with coordinates ( -10 , -8 ) and B with coordinates ( -5 , 4 )

  • To calculate - distance between the two points

The distance formula states that

[tex]d(AB) = \sqrt{(x_{2} - x_{1}) {}^{2} + (y _{2} - y_{1}) {}^{2} } \\ [/tex]

from the question , we can make out that

[tex]x_{1} = - 10 \\ x_{2} = - 5 \\ y_{1} = - 8 \\ y_{2} = 4[/tex]

substituting the values in the formula , we get

[tex]d(AB) = \sqrt{( - 10 - ( - 5)) {}^{2} + ( - 8 - 4) {}^{2} } \\ \\ \implies \: d(AB) = \sqrt{( - 10 + 5) {}^{2} + ( - 8 - 4) {}^{2} } \\ \\ \implies \: d(AB) = \sqrt{( - 5) {}^{2} + ( - 12) {}^{2} } \\ \\ \implies \: d(AB) = \sqrt{25 + 144} \\ \\ \implies \: d(AB) = \sqrt{169} \\ \\ \implies \: d(AB) = 13 \: units[/tex]

therefore , option 3) 13 is correct !

hope helpful ~

Let A: (-10,-8) and B: (-5,4)

X_1: -10

Y_1: -8

X_2: -5

Y_2: 4

Following the Distance formula:-

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

Let's plug in the numbers into the formula

[tex]\tt \: \sqrt{ (- 5 - (- 10))^{2} (4 - ( - 8))} [/tex]

[tex]\tt \: = \sqrt{ - 5 + 10) ^{2} + (4 + 8) ^{2} } [/tex]

[tex]\tt \: = \sqrt{(5)^{2} + (12) ^{2} } [/tex]

[tex]\tt \: = \sqrt{25 + 144} [/tex]

[tex] \tt \: = \sqrt{169} [/tex]

[tex] \tt = 13[/tex]

Therefore, our answer is option 3) 13!!!

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