Question

Round to the nearest tenth if necessary

Find the distance between the two points: (-10,-8), (-5,4)

1. 169
2.16
3.13
4.17

Answer 1

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

X_1: -10

Y_1: -8

X_2: -5

Y_2: 4

Following the Distance formula:-

`\boxed{\tt ab = \sqrt{(x_2 - x_1)^(2) (y_2 - y_1)^(2) } }`

Let's plug in the numbers into the formula

`\tt \: \sqrt{ (- 5 - (- 10))^(2) (4 - ( - 8))}`

`\tt \: = \sqrt{ - 5 + 10) ^(2) + (4 + 8) ^(2) }`

`\tt \: = \sqrt{(5)^(2) + (12) ^(2) }`

`\tt \: = √(25 + 144)`

`\tt \: = √(169)`

`\tt = 13`

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

Answer 2

`\huge\underline\mathcal{\red{A}\purple{n}\orange{s}\blue{w}\green{e}\pink{r} -}`

• 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

`d(AB) = \sqrt{(x_(2) - x_(1)) {}^(2) + (y _(2) - y_(1)) {}^(2) } \\`

from the question , we can make out that

`x_(1) = - 10 \\ x_(2) = - 5 \\ y_(1) = - 8 \\ y_(2) = 4`

substituting the values in the formula , we get

`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) = √(25 + 144) \\ \\ \implies \: d(AB) = √(169) \\ \\ \implies \: d(AB) = 13 \: units`

therefore , option 3) 13 is correct !

hope helpful ~