Question

Given a triangle with coordinates X(2, -1), Y(-5, -4), and Z (-2. 3), what type of triangle is it? equilateralisosceles rightscalene

Answer 1

First, let´s calculate the length of the sides of the triangle, by calculating the distance between the given points.

Use the following formula:

$d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}$

where (x1,y1) and (x2,y2) are the limits of a segment with length d.

Then, the ditance between points X and Y is;

$d_{XY}=\sqrt[]{(-5-2)^2+(-4-(-1))^2}=\sqrt[]{49+9}=\sqrt[]{58}$

The distance between points Y and Z is:

$d_{YZ}=\sqrt[]{(-2-(-5))^2+(3-(-4))^2}=\sqrt[]{9+49}=\sqrt[]{58}$

and the distance between points Z and X is:

$d_{ZX}=\sqrt[]{(2-(-2))^2+(-1-3)^2}=\sqrt[]{16+16}=\sqrt[]{32}$

Then, you have two sides with the same length, which are sides XY and YZ and another side with a different length.

When a triangle has two sides with the same length, such a triangle is isosceles.