Chapter 19: Coordinate Geometry

what are the x and y coordinates in quadrant I?

both coordinates are positive

what are the x and y coordinates in quadrant II?

the x coordinate is negative and the y coordinate is positive

what are the x and y coordinates in quadrant III?

both coordinates are negative

what are the x and y coordinates in quadrant IV?

the x coordinate is positive and the y coordinate is negative

what does the x and y mean in the coordinate pair in terms of movement?

x is the right/left movement

y is the up/down movement

the four quadrants are labeled in which direction?

counter clockwise

true or false: only two points are needed to define a specific line

true

the slope of line provides us with the measure of the “________” of the line

steepness

what is the equation for the slope of a line?

change in y over change in x

y2-y1/x2-x1

what kind of slope does a vertical line have?

undefined slope

what kind of slope does a horizontal line have?

zero slope

a line that is pointing up, moving from left to right has a _________ slope

positive

a line that is point down, moving from left to right has a ________ slope

negative

lines with positive slopes always intersect quadrants

I and II

a positively sloped line intersects quadrant IV only if

its x-intercept is positive

a positively sloped line intersects quadrant II only if its

x intercept is negative

if a line has an x-intercept is 0, then the positively sloped line will intersect only quadrants

I and III

negatively sloped lines always intersect quadrants

II and IV

a negatively sloped line intersects quadrant I only if its

x-intercept is positive

a negatively sloped line intersects quadrant III only if its

x-intercept is negative

if a line’s x-intercept is zero, then the negatively sloped line will intersect only quadrants

II and IV

the slope of any horizontal line is

0

if the y-intercept of a horizontal line is positive, the line intersects only quadrants

I and II

if the y-intercept of a horizontal line is negative, the line intersects only quadrants

III and IV

the slope of any vertical line is

undefined

a vertical line has either ____ y-intercept or _____ ______ y-intercepts

no, infinitely many

she large the absolute value of the slope of a line, the _________ the line

steeper

true or false: whether a line has positive or negative slope does not affect how steep the line is

true

what is the slope intercept equation?

y = mx +b

what is the m in the slope intercept equation?

the slope

what is the b in the slope-intercept equation?

the y-intercept

if a point is on a line, then the coordinates of the point must

satisfy the equation of the line

before identifying any components in a line’s equation, you must first isolate

the y-term

what is the equation of a vertical line?

x= a where a is the x-intercept of that line

the equation of a horizontal line is

y=b where b is the y-intercept of that line

what is the standard form of the equation of a line?

Ax + By = C

parallel lines have the same

slope

parallel lines have different

y-intercepts

any pair of perpendicular lines creates four

right angles

two perpendicular lines have slopes that are

negative reciprocals of one another

(x,y) reflected over the x-axis becomes

(x, -y)

(x,y) reflected over the y axis becomes

(-x,y)

(x,y) reflected over the origin becomes

(-x,-y)

what is the distance formula?

√(x₂-x₁)² + (y₂-y₁)²

how do you use a right triangle to calculate the length of a line segment?

sketch a right triangle with the line segment as the hypotenuse and apply the pythagorean theorem: a²+b² = c²

if two points share the same y-coordinate as in (x,y) (z,y) then the distance between them is the

absolute value of x-z

what is the midpoint formula?

(x₁+x₂ / 2, y₁+y₂ /2)