length of AC = 15 (option A)
Explanation:
We use the cordinates of A and C to find the distance of AC.
A = (-6, -5)
C = (6, 4)
The length of AC = distance of AC
Distance formula:
[tex]dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} x_1=-6,y_1=-5,x_2=6,y_2\text{ = }4 \\ \text{distance AC = }\sqrt[]{(4-(-5))^2+(6-(-6))^2} \\ =\text{ }\sqrt[]{(4+5)^2+(6+6)^2} \end{gathered}[/tex][tex]\begin{gathered} =\text{ }\sqrt[]{(4+5)^2+(6+6)^2}\text{ = }\sqrt[]{9^2+12^2} \\ \text{Distance AC = }\sqrt[]{81+144}\text{ = }\sqrt[]{225} \\ \text{Distance AC = 1}5 \\ \text{length of AC = }15\text{ (option A)} \end{gathered}[/tex]
