Question

Triangle ABC is given by the following points: A(-4,1), B(5,3) and C(3,-5). Is Triangle ABC scalene, isosceles, or equilateral?

Answer 1

We are given three points of a triangle and required to find out the nature of the triangle that they form the vertices of.

Our approach is to get the distance between the points to make our inference.

3 equal sides will give us an equilateral triangle

2 equal sides will give us an isosceles triangle

3 equal sides will give us a scalene triangle

Now we find the distance between the points, i.e. the length of the sides.

The general formula to get the length of the line is:

`\sqrt[]{(y_2-y_1_{})^2+(x_2-x_1_{})^2}`

Line AB:

`\sqrt[]{(3-1)^2+(5-(-4))^2}=\sqrt[]{2+9}=\sqrt[]{85}`

Line BC:

`\sqrt[]{(-5-3)^2+(3-5)^2}=\sqrt[]{64^{}+4}=\sqrt[]{68}`

Line AC:

`\sqrt[]{(-5-1)^2+(3-(-4))^2}=\sqrt[]{36^{}+49}=\sqrt[]{85}`

From these, we can see that two lines in the triangle are equal.

Our triangle is an isosceles one.