The points A(0, 6), B(-5, 3), and C(3,1) are the vertices of a triangle. This triangle is-

Correct option is C

Given:

The points A(0, 6), B(-5, 3), and C(3,1) are the vertices of a triangle. 

Formula used:

Distance between two points , $$(x_1, y_1)$$​ and  $$(x_2, y_2)$$​ = $$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

Solution:

Length of AB, 

AB = $$\sqrt{(-5 - 0)^2 + (3 - 6)^2}$$​​

AB = =$$\sqrt{25 + 9}$$​​

AB = $$\sqrt{34}$$​

Length of BC,

BC = $$\sqrt{(3 - (-5))^2 + (1 - 3)^2}$$​

BC = $$\sqrt{64 + 4}$$​

BC = $$\sqrt{68}$$​
Length of CA,

CA = $$\sqrt{(0 - 3)^2 + (6 - 1)^2}$$​​

CA = $$\sqrt{9 + 25}$$​

CA = $$\sqrt{34}$$

So, AB and CA have equal length and BC is different.

Then Triangle is isosceles.

Thus, the correct answer is (c).