Question

Show that the point A(-5,2),and B(2,5) C(5,2)are the vertices of a scalene triangle.

Answer 1

Answer:

See the explanation

Step-by-step explanation:

Concept : Distance between the points P$(x_1,y_1)$ and Q$(x_2,y_2)$ is

                                   $\sqrt {(x_2-x_1)^2+(y_2-y_1)^2}$

Thus with given coordinates

                       AB $=\sqrt{(2+5)^2+(5-2)^2}=\sqrt{49+9}=\sqrt {58}$

                       BC $=\sqrt{(5-2)^2+(2-5)^2}=\sqrt{9+9}=\sqrt {18}$

                       CA $=\sqrt{(5+5)^2+(2-2)^2}=\sqrt{100+0}=10$

Clearly all the side lengths are unequal, so triangle is scalene