Answer to Question #293929 in Analytic Geometry for bookaddict

Question

a. The points 𝐴,𝐵 and 𝐶 have co-ordinates (−1,2),(1,1) and (2,3) respectively. Sketch the triangle 𝐴𝐵𝐶. By calculating the lengths of the sides of this triangle, determine if it is scalene, isosceles, or equilateral.

Answer 1

$$AB=\sqrt{(1-(-1))^2+(1-2)^2}=\sqrt{5}$$

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

$$AC=\sqrt{(2-(-1))^2+(3-2)^2}=\sqrt{10}$$

The triangle ABC is isosceles.