Question

The triangle formed by the points (2,3)(5,4)and (6,7) is which triangle ​

Answer 1

Answer:-

The triangle formed by the points (2,3)(5,4)and (6,7) is an isosceles triangle.

Answer 2

Answer:

It is an isosceles triangle.

Step-by-step explanation:

To find the type of the triangle, we find the length of the sides of the triangle.

Let (2,3) be point A, (5,4) be point B and (6,7) be point C

We know that according to the distance formula,

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

where, (x₁,y₁) and (x₂,y₂) are two points

Therefore, here AB =  $\sqrt{(2-5)^2 + (3-4)^2$

                                =  $\sqrt{(-3)^2 + (-1)^2$

                                =  $\sqrt{9 +1$

                                = $\sqrt {10}$

Similarly,  BC =  $\sqrt{(2-5)^2 + (3-4)^2$

                      =  $\sqrt{(-1)^2 + (-3)^2$

                      =  $\sqrt{1+9$

                      = $\sqrt {10}$

Similarly,  CA =  $\sqrt{(6-2)^2 + (7-3)^2$

                      =  $\sqrt{(4)^2 + (4)^2$

                      =  $\sqrt{16 +16$

                      = $\sqrt {32}$

                      = $4\sqrt {2}$

As AB = BC

=> The two sides of the triangle are equal, therefore, it is an isosceles triangle.