Question

Find the distance between the two points in simplest radical form. (7,-1) and (9,-9)

Answer 1

Answer:

$\sqrt{68}$

Step-by-step explanation:

(7 , -1) = (x1 , y1)

(9 , -9) = (x2 , y2)

distance formula = $\sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

=$\sqrt{(9 - 7)^2 + (-9 - (-1))^2}$

=$\sqrt{2^2 + (-9 + 1)^2}$

=$\sqrt{4 + (-8)^2}$

=$\sqrt{4 + 64}$

=$\sqrt{68}$

Answer 2

Answer:

$Distance = \sqrt{ 68 } \\\\or \\\\Distance =2 \sqrt{17}$

Step-by-step explanation:

$Let \ (x_1 , y_1) = ( 7 , - 1 ) \ and \ (x_2, y _ 2 ) = ( 9 , - 9 )\\\\\\Distance = \sqrt{(x_2 - x_ 1)^2 + (y_ 2 - y_ 1)^2}$

               $= \sqrt{(9 - 7)^2 + ( -9 --1)^2} \\\\=\sqrt{2^2 + ( -9 + 1)^2 }\\\\=\sqrt {4 + (-8)^2 }\\\\=\sqrt{ 4 + 64 }\\\\=\sqrt{68}\\\\= \sqrt { 4 \times 17}\\\\=\sqrt{2^2 \times 17}\\\\=2 \sqrt{17}$