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, -10) and (2, 2) so the slope becomes:

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y - 3)(y + 2)
(y x y) + (y x 2) + (-3 x y) + (-3 x 2)
y² + 2y - 3y - 6
y² - y - 6

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 = \( \sqrt{a} \) = \( \sqrt{9} \) = 3

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 = 3² + 3²
c² = 18
c = \( \sqrt{18} \) = \( \sqrt{9 x 2} \) = \( \sqrt{9} \) \( \sqrt{2} \)
c = 3\( \sqrt{2} \)

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

c² = a² + b²
c² = 3² + 5²
c² = 9 + 25
c² = 34
c = \( \sqrt{34} \)

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 8 x 8 = \( \frac{64}{2} \) = 32