Answer:
[tex]5 \sqrt{5} [/tex]
Step-by-step explanation:
We want to find the distance between (-8,-4) and (2,-9).
We use the distance formula:
[tex]d = \sqrt{ {(x_2-x_1)^2} +(y_2-y_1)^2 } [/tex]
We substitute the coordinates to get:
[tex]d = \sqrt{ {(2- - 8)^2} +( - 9 - - 4)^2 } [/tex]
We simplify to obtain:
[tex]d = \sqrt{ {(2 + 8)^2}+( - 9 + 4)^2 } [/tex]
Add the numbers within the parenthesis to get:
[tex]d = \sqrt{ {(10)^2}+( -5)^2 } [/tex]
Find the squares of the numbers under the radical
[tex]d = \sqrt{ {100}+25} [/tex]
[tex]d = \sqrt{125} = 5 \sqrt{5} [/tex]
