Answer:
AB is A
BC is B
AC is D
Step-by-step explanation:
To find the length of each side, use the formula for the distance between coordinate pairs.
We can find the distance using the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AB
We then substitute (-3,6) as [tex](x_1,y_1)[/tex] and (2,1) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(2--3)^2+(1-6)^2} \\d=\sqrt{(2+3)^2+(-5)^2} \\d=\sqrt{25+25}\\d=\sqrt{50}[/tex]
BC
We then substitute (2,1) as [tex](x_1,y_1)[/tex] and (9,5) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(9-2)^2+(5-1)^2} \\d=\sqrt{(-7)^2+(4)^2} \\d=\sqrt{49+16}\\d=\sqrt{65}[/tex]
AC
We then substitute (-3,6) as [tex](x_1,y_1)[/tex] and (9,5) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(9--3)^2+(5-6)^2} \\d=\sqrt{(12)^2+(-1)^2} \\d=\sqrt{144+1}\\d=\sqrt{145}[/tex]
