Solving for the Distance between two Points
Answer:
[tex]4\sqrt{5}[/tex]
Step-by-step explanation:
If you have the two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], the distance, [tex]d[/tex], between them can be calculated by [tex]d = \sqrt{(x_2 -x_1)^2 +(y_2 -y_1)^2}[/tex].
In this case, point [tex]A[/tex] has the coordinates [tex](3,0)[/tex] and point [tex]C[/tex] has the coordinates [tex](7,-8)[/tex]. We can finally solve for the length by finding the distance between them.
[tex]AC = \sqrt{(7 -3)^2 +(-8 -0)^2} \\ AC = \sqrt{4^2 +(-8)^2} \\ AC = \sqrt{16 +64} \\ AC = \sqrt{80} \\ AC = \sqrt{4 \cdot 4 \cdot 5} \\ AC = 4\sqrt{5}[/tex]
