The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 3) and (2, 1) so the slope becomes:

m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(1.0) - (3.0)}{(2) - (-2)} \) = \( \frac{-2}{4} \)
m = -\(\frac{1}{2}\)

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 6² + 5²
c² = 36 + 25
c² = 61
c = \( \sqrt{61} \)

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{81} \) = 9

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 9² + 9²
c² = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)

The area of a rectangle is equal to its length x width:

a = l x w
a = a x b
a = 6 x 4
a = 24

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

7a⁴ + 8a⁴ = 15a⁴