Ch. 18 Coordinate Geometry Flashcards
Slope
m = (Y2 - Y1) / (X2 - X1)
The greater the absolute value, the ____ (steeper/ flatter) the slope is.
Steeper
Small abs value = flatter
Slope-intercept equation
y = mx + b
y – y coordinate
m – slope
x – x coordinate
b – y-intercept
How to determine x-intercept
Use y = mx + b
Make y = 0, solve for x.
(when y is 0, that’s where the line will intercept the x-axis)
How to determine if point A(x,y) is on a certain line.
Plug coordinates x & y from Point A into the equation: y = mx+b
If it’s still equal, then the point is on the line
Information needed to define a line
y = mx+b
1. One point on the line AND
2. Slope of the line (or slope of a line that’s parallel or perpendicular to the line)
OR
2. A second point on the line (y-int, x-int, or any other point) - to determine the slope
Parellel line equations
Same slope, different y-int
same m; different b
y = 4x + 3
y = 4x - 1/2
Perpendicular line equations
The product of their slopes is -1
(Their slopes are negative reciprocals)
Reflection over the x-axis
(x,y) –> (x, -y)
Reflection over the y-axis
(x,y) –> (-x, y)
Reflection over the origin
(x,y) –> (-x,-y)
Reflection over the line y = x
(x,y) –> (y,x)
Reflection over the line y = -x
(x,y) –> (-y,-x)
Reflection over the line y = b where b is any constant
(x,y) –> (x, 2b-y)
Reflection over the line x = a where a is any constant
(x,y) –> (2x-a, y)
Distance between two points (x1, y1) and (x2, y2)
d = √(x2 - x1)^2 + (y2 - y1)^2
(can use pythagorean theorem to derive)
If two points have the same x- or y- coordinates, how do you calc distance?
Absolute value of the difference
Midpoint formula
xm, ym = (x1+x2) / 2 , (y1 + y2) / 2
Midpoint is average of coordinates
Equation for a circle in the coordinate plane
Let (a,b) be the center of the circle & r be the radius:
(x - a)^2 + (y - b)^2 = r^2
(can use distance formula to derive, let (x, y) be any point on the circle)
When we reflect points (x,y) over point (a,b), (x,y) becomes what?
(x, y) –> (2a - x, 2b - y)
