The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

9b - 1 = \( \frac{b}{-9} \)
-9 x (9b - 1) = b
(-9 x 9b) + (-9 x -1) = b
-81b + 9 = b
-81b + 9 - b = 0
-81b - b = -9
-82b = -9
b = \( \frac{-9}{-82} \)
b = \(\frac{9}{82}\)

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

y² - 2y - 24 = 0
(y + 4)(y - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 4) or (y - 6) must equal zero:

If (y + 4) = 0, y must equal -4
If (y - 6) = 0, y must equal 6

So the solution is that y = -4 or 6

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

a = ½bh
a = ½ x 6 x 9 = \( \frac{54}{2} \) = 27