Coordinate Geometry

A slope of m=2, could be..

2/1. -2/-1 or 2K/1K. All are the same

When the slope a line is 1 or -1, meaning that y=x or y=-x, then the degree formed by the slope is

45 degrees

Points that lie on the same line, and when connected form a straight line is ...

Collinear; (any two points are always collinear). but If you cannot connect a series of points with a straight line then, the points are Non collinear. (only three or more points can be noncollinear)

Two points determines a ...

Line

Remember that a variable can have either

a positive or negative value.

A horizontal line has a slope of

zero, 0/x

Coordinate pairs are in the form of ...

(x,y) alphabetical order

A line that passes through the origin, has a x and y-intercept at

0

Line segment

A finite piece of a line, or a part of a line with two endpoints, where there is an infinite set of points between the end points.

Plane

A flat expanse of points expanding in every direction. It has a width and length, but no depth.

Four points can determine

A pair of parallel or skewed lines, a plane, and one other coplanar/noncoplanar point.

Line

A set of continuous points that extends indefinitely in opposite directions

The "y" axis moves

Up and down, Vertically

Point

a location in space that indicates a position, but occupies no space and has no dimension

Every point plotted on an x and y plane, lies either within ...

a quadrant or on an axis.

When the prompt asks to find how many distinct points exist on a line segment, your first move should be to create ...

an equation for the line, and then find the x or y values that satisfies the criteria of the prompt.

A slope is positive if it rises from..

left to right

A slope is negative if it descends from..

left to right, or rises from right to left.

A slope and a point is enough to create a ...

linear equation

Within the graph of a parabola,the line of symmetry acts a ..

mirror line which reflects the the points to create a symmetric graph.

Slopes of perpendicular lines are ..

negative reciprocal of each other. In other words the first slope is rotated 90 degrees to create the second slope, which makes them perpendicular to one another.

Slope of a line is the measure...

of a line's incline, or it is defined as the ratio rise over run , or it is defined as the ratio change in y over the change in x, or it is defined as the ratio height over length. The formula is (y2-y1)/(x2-x1)

The graph of a quadratic shows shape known as a...

parabola, which is a unique "u" shape graph.

If a point is plotted on a plane, and then a mirror image of the point is plotted with a mirror line between both points and a segment drawn between both points , then the mirror line acts as ...

perpendicular bisector of the segment, as each point is equidistant from the mirror line.

Three non-collinear points, determines a ...

plane. where points that are collinear are also coplanar.

You can graph a line on the x and y plane by ...

plotting individual points.

The quadrant dictates the ...

positive or negative sign of a point.

Remember that a distance is always ...

positive value

Remember when dealing with triangles while solving for the side lengths, it is easiest to scale down to simplify calculations, just remember to

scale back up at the end of the calculation to insure the proportions match.

Remember that when a triangle is named, it is named clockwise or counter clockwise. When an angle is associated with the naming of the triangle, the angle is generally sitting at the ...

second vertices named in the triangle. For example, Triangle <ABC = 90 degrees, which means that the 90 degree angle sits at vertices B. Very important!!

Keep in mind that line y=x is unique in that it creates a boundary line that ...

separates certain x and y points. All points above the y=x line are such that all y values are greater than the x value, and all points below the y=x line are such that all y values are less than the x values. Along the y=x line all values of x equal their y value counter parts.

You can think of slopes as a form of ratio between rise and run, which means if you know the slope and one of the distances between the two x value points, or two y value points, you can...

set up a proportion that relates the slope of the line to the change in "y" over the change in "x"

The x-intercepts of the quadratic equation is the ...

solutions of the equation, which can be found by setting the equation equal to zero. There can be 2, 1 or no solution.

When searching for the distance between two points on the same horizontal or vertical line, simply ...

subtract the the x-values of the two points, or the y-values depending on whether you are solving for the y or the x distance.

When a point is reflected over a line with the equation y = -x, the x and y values of the original coordinate point are ...

switched in the coordinate points of the reflected point, they will have alternate positive and negative coordinates as well. So 2,5 reflected over y = -x has a coordinate point of -5,-2

When a point is reflected over a line with the equation y = x, the x and y values of the original coordinate point are ...

switched in the coordinate points of the reflected point. So 1,2 reflected over y = x has a coordinate point of 2,1

When searching for the distance between two points that create a slanted line, remember that solving for the length of a slanted line always means...

that we should use the Pythagorean Theorem, where the slanted line should always represent the hypotenuse.

Any equation that has y or x to the first power, must be ...

the equation of a line, or must be linear equation.

For a circle graphed in the x-y plane, think of the radius as the slope of a line,or ...

the hypotenuse a triangle, and solve it using the Pythagorean Theorem.

The x-intercept is where ...

the line crosses the x axis or where "y" equals zero. Ex: (x,0)

The y-intercept is where ...

the line crosses the y axis or where "x" equals zero. Ex: (0,y)

Slopes of parallel lines are...

the same, they rise the same amount over the same distance

You can solve linear equations graphically by using ...

the slope and proportions.

Distance formula in a coordinate plane is...

the square root of, change in "x" squared + change in "y" squared.

Point interception is where ..

two lines are equal, and a point shared by both lines.

A vertical line has a slope that is

undefined, y/0, you cannot climb a vertical line

Every line plotted on a graph has its own ...

unique equation that defines its x and y intercepts and slope.

The equation y=x^2 produces a parabola whose ...

vertex sits at the origin of the x and y plane.

Each parabola has a line of symmetry at the ....

vertex, which is the highest point on a parabola opening downward, or the lowest point on a parabola opening upward.

A vertical line at the x-axis, has the equation ...

x = 0, and it only has an x-intercept.

A vertical line at point 4 has the equation ...

x= 4, because it only has a "x intercept. In a vertical line, you will have a constant x-value, and an infinite number of y-values.

A Quadratic expression is one in which the highest power of ...

x^2

The equation of a circle with center 0,0 and with radius "r" is ...

x^2 + y^2 = r^2, which is really the Pythagorean Theorem with the radius replacing the hypotenuse.

A horizontal line at the y-axis, has the equation ...

y = 0, , and it only has a y-intercept.

A horizontal line at point -3 has the equation ...

y= -3, because it only has a "y-intercept". A horizontal line will have a constant y-value , and an infinite number of x-values. .

Slope intercept form equation

y= mx+B, where "m" is the slope, and "b" is the y-intercept

The "x" axis moves ...

From left to right, Horizontally

For the linear equation, y=x the line behaves by ...

Passing through the origin, producing a 45 degree angle, and all x and y values are identical.

The standard equation for the quadratic of a line is ...

ax^2 + bx + c, where if a>o the parabola opens upward, and if a<0 the parabola opens downward. Also if the absolute value of a is > 1 the then the parabola is skinny, but if the absolute value of a is < 1 then the parabola is wide.

All points on a coordinate plan are ...

coplanar

Quadrants are named ...

counterclockwise, starting from the upper right quadrant.

When dealing with circles on the x-y plane, remember that when the circle is in a position where it intercepts the x axis twice, then the distances between each intercept and the center point are ...

equal, which means you are dealing with and Isosceles right triangle. Using algebra that relates sides and point maybe the best way to solve problems such as this.

Every point on a line must satisfy the ...

equation of that specified line.

Remember that every point on a perpendicular bisector of a segment is ...

equidistant from the two end points of that segment.

Any two points that has the same Y coordinate falls on the same horizontal line, and any two points that has the same x coordinate..

falls on the same vertical line.

When writing the equation of a line you must first..

find the slope, then select a point, plug the point and slope into the slope-intercept formula to find the y-intercept, then write the equation of the line. From there you can use the equation of a line to solve for any point on that line.

So if we choose point -5,3 and -3,5 we can see that the point is being reflected over the line with equation y = -x. So any (x,y) point chosen on the y = -x equation line, along with the endpoints of the segment created between the two points would ...

form an isosceles triangle.

So if we choose point 1,7 and 7,1 we can see that the point is being reflected over the line with equation y = x. So any (x,y) point chosen on the y = x equation line, along with the endpoints of the segment created between the two points would ...

form an isosceles triangle.

When the slope a line is greater than 1, then the degree formed by the slope is

greater than 45 degrees, which means the slope incline is steeper.

If we reflect a point over the x-axis, then the original point and the reflected point will ...

have the same x coordinate ( vertical line), but they will have alternate positive and negative y coordinates.

If we reflect a point over the y-axis, then the original point and the reflected point will ...

have the same y coordinate (horizontal line), but they will have alternate positive and negative x coordinates.

If a circle is centered at the origin of an "x" and "y" plane, the slope of each radius has a ...

horizontal leg which is the absolute value of "x", and a vertical leg which the absolute value of "y".

When dealing with a quadratic equation such as ax^2 + c, the "c" represents the constant, which dictates ...

how high or low the parabola moves on the y axis. Remember that y=mx + B, B is the y-intercept.