Here are the theorems, facts, and definitions that could help tomorrow on the quiz or test whatever it's going to be.

Geometry Chapter 13

Theorem 13-1: The Distance Formula

The distance between points (x_{1}, y_{1}) and (x_{2}, y_{2}) is given by:

d= √ (x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}

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Theorem 13-2: An equation of the circle with center (a,b) and radius r is

(x-a)^{2} + (y-b)^{2} = r^{2}

^{ }

To find the slope of a line:

Slope m= __y___{2}__-y___{1}

x_{2}-x_{1}

_{ }

Facts:

Lines with positive slope rise to the right

Lines with negative slope fall to the right

The greater the absolute value of a line’s slope, the steeper the line

The slope of a horizontal line is zero

The slope of a vertical line is not defined

Theorem 13-3:

Two non-vertical lines are parallel if and only if their slopes are equal

Theorem 13-4:

Two non-vertical lines are perpendicular if and only if the product of their slopes is -1.

m_{1} * m_{2} = -1, or m_{1} = - 1/m_{2}

Theorem 13-5: The Midpoint Formula

The midpoint of the segment that joins points (x1, y1) and (x2, y2) is the point

( __x___{1}__ + x___{2} , __y___{1}__+y___{2} )

2 2

Theorem 13-6: Standard Form

The graph of any equation that can be written in the form

Ax + By = C

Where A and B are not both zero, is a line

Theorem 13-7: Slope-Intercept Form

A line with the equation y =mx + b has slope m and y-intercept b

Theorem 13-8: Point-Slope Form

An equation of the line that passes through the point (x1, y1) and has slope m is

Y – y_{1} = m(x - x_{1})

Terms to know:

Slope: the ratio of the change in y (vertical change) to the change in x (horizontal change).

Vector: Any quantity such as force, velocity, or acceleration that has both magnitude (size) and direction.

Magnitude of a vector: The length of the arrow from point A to point

B and is denoted by the symbol

|AB |

Scalar multiple of vectors: The product of the vector (a,b) and the real number k is the scalar multiple (ka, kb).

Linear equation: and equation whose graph is a line

Dot product: For vectors (a,b) and (c,d), the number ac+bd. The dot product of perpendicular vectors is zero.

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Note from Karla: The format is a little bit changed. All you have to be aware of is that the subscript of the formulas like the 1s and the 2s that are in-between the division line are not supposed to be there. They're supposed to be above the division line. So do not get confused by that.

Another thing, in the magnitude of a vector definition, AB is a ray, The line just didn't show up.

Good Luck!