Respuesta :
Answer:
The length of side AB is [tex]\sqrt{50}[/tex] units.
The length of side BC is [tex]\sqrt{65}[/tex] units.
The length of side AC is [tex]\sqrt{145}[/tex] units.
Step-by-step explanation:
To find the length of each side, we use the formula for the distance between two points.
Distance between two points:
Points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Side AB:
Points [tex]A(-3,6),B(2,1)[/tex]. So the distance between them is:
[tex]D = \sqrt{(2-(-3))^2 + (1-6)^2} = \sqrt{50}[/tex]
The length of side AB is [tex]\sqrt{50}[/tex] units.
Side BC:
Points [tex]C(9,5),B(2,1)[/tex]. So the distance between them is:
[tex]D = \sqrt{(2-9)^2 + (1-5)^2} = \sqrt{65}[/tex]
The length of side BC is [tex]\sqrt{65}[/tex] units.
Side AC:
Points [tex]A(-3,6),C(9,5)[/tex]. So the distance between them is:
[tex]D = \sqrt{(9-(-3))^2 + (5-6)^2} = \sqrt{145}[/tex]
The length of side AC is [tex]\sqrt{145}[/tex] units.
