Answer:
[tex]D = 3\sqrt{2}[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (3,-4)[/tex]
[tex](x_2,y_2) = (6,-7)[/tex]
Required
Determine the distance between the two points
Distance (D) is calculated as:
[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Substitute values for x's and y's
[tex]D = \sqrt{(6 - 3)^2 + (-7 - (-4))^2}[/tex]
[tex]D = \sqrt{(6 - 3)^2 + (-7 +4)^2}[/tex]
[tex]D = \sqrt{(3)^2 + (-3)^2}[/tex]
[tex]D = \sqrt{9+9}[/tex]
[tex]D = \sqrt{18}[/tex]
Express as 9 * 2
[tex]D = \sqrt{9*2}[/tex]
Split:
[tex]D = \sqrt{9}*\sqrt{2}[/tex]
[tex]D = 3*\sqrt{2}[/tex]
[tex]D = 3\sqrt{2}[/tex]
