Question

Find the distance between the two points and simplest rational form (3,-4) (6,-7))

Answer 1

Answer:

$D = 3\sqrt{2}$

Step-by-step explanation:

Given

$(x_1,y_1) = (3,-4)$

$(x_2,y_2) = (6,-7)$

Required

Determine the distance between the two points

Distance (D) is calculated as:

$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Substitute values for x's and y's

$D = \sqrt{(6 - 3)^2 + (-7 - (-4))^2}$

$D = \sqrt{(6 - 3)^2 + (-7 +4)^2}$

$D = \sqrt{(3)^2 + (-3)^2}$

$D = \sqrt{9+9}$

$D = \sqrt{18}$

Express as 9 * 2

$D = \sqrt{9*2}$

Split:

$D = \sqrt{9}*\sqrt{2}$

$D = 3*\sqrt{2}$

$D = 3\sqrt{2}$