Question

How do you use the distance formula and slope formula to classify a triangle

Answer 1

see the distance formula to find the length of the sides...
opposite sides equal it could be a rectangle or parallelogram
all sides equal, square or rhombus
adjacent equal, kite
and then the slope is used to check angles
if the product of the 2 lines in -1 the lines are perpendicular (right angle)
the the slopes of 2 lines are the same the sides are parallel.
hope it helps

Answer 2

Explanation:

Below are different types of triangles:-

• Equilateral triangle - All the three sides are of equal length
• Isosceles triangle -  Two sides are equal
• Scalene triangle -  All the three sides are of different length
• Right triangle - One angle is 90 degrees

We can find the length of the three sides by using the distance formula.

The distance formula is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

If the length of all three sides are equal then it will be an equilateral triangle.

If the length of any two sides are equal then it will be an isosceles triangle.

If the length of all sides are different then it will be scalene triangle.

Now, using the slope formula, we can find whether the triangle is right triangle or not.

Slope formula is given by $m=\frac{y_2-y_1}{x_2-x_1}$

If the product of any two slopes is -1. then the angle between them is 90 degrees and hence can be classified as a right triangle.