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

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

Explanation:

Below are different types of triangles:-

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

The distance formula is

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

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.

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step-by-step explanation:

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the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places