Question

the coordinates of the vertices of triangle ABC are a (-2,2), b (5,-3), c (-4,-1). Identify the perimeter of triangle ABC.

Answer 1

The formula of a distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

`A(-2,\ 2);\ B(5,\ -3)\\\\AB=√((5-(-2))^2+(-3-2)^2)=√(49+25)=√(74)\\\\A(-2,\ 2);\ C(-4,\ -1)\\\\AC=√((-4-(-2))^2+(-1-2)^2)=√(4+9)=√(13)\\\\B(5,\ -3);\ C(-4,\ -1)\\BC=√((-4-5)^2+(-1-(-3))^2)=√(81+4)=√(85)\\\\P_(\triangle ABC)=√(74)+√(13)+√(85)`