Coordinate Geometry Flashcards
What are the different quadrants of the xy-plane?
Starting in the top right I, II, III, IV (going counter clockwise)
How do you calculate the slope of a line?
Rise/run
Change in y / change in x
(Y2 - Y1) / (X2 - X1)
Lines with positive slopes move in which direction and which quadrants must it intersect?
Upwards
Quadrants I and III
What should you know about horizontal lines?
They have a slope of zero and the y coordinate is always the same.
What should you know about vertical lines?
The have the same x coordinate and have an undefined slope.
The larger the absolute value of a slope…
The steeper it is
What is the slope intercept equation?
y=Mx + b
Where m is the slope, x is the corresponding x coordinate for the point on the line, y is the y coordinate for a point on the line and b is the y intercept of the line.
At the x intercept, the value of y is what? And what is the coordinate pair?
0 and the coordinate pair is always (x,0)
If you know the slope and y-intercept, what else do you also know?
The x intercept (-b/m)
What is the equation of the x axis?
Y=0
What is the equation of the y axis?
x=0
What is the equation of a horizontal line?
y=b, where b is the y intercept
What is the equation of a vertical line?
x=a where a is the x intercept of the line
What is the standard form of an equation?
Ax + By = C
Where A,B, and C are constants.
What info do you need to define a line?
1) a point on that line
2) the slope of that line or the slope of a line that is parallel or perpendicular to that line
3) another point on that line (eg x intercept, y intercept, or any other point)
Parallel lines have:
The same slope but a different y intercept so they never intersect
What must you know about perpendicular lines?
They intersect at 90 degrees and create 4 right angles. Their slopes are negative reciprocals of each other and multiply to -1
How do you reflect point (x,y) over the x axis?
(x,-y)
How do you reflect point (x,y) over the y axis?
(-x,y)
How do you reflect point (x,y) over the origin?
(-x,-y)
Reflection over the line y=x: what is the image when point (x,y) is reflected?
(y,x)
Reflection over the line y=-x: what is the image when point (x,y) is reflected?
(-y,-x)
Reflection over the line y=b: what is the image when point (x,y) is reflected?
(x,2b-y)
Reflection over the line x=a: what is the image when point (x,y) is reflected?
(2a-x,y)
How do you calculate the distance between 2 points using the distance formula?
Square root of:
(change in x)^2 + (change in y)^2
When do you not have to use the distance formula when finding the distance between two coordinates and what do you do to find the distance instead?
When the two coordinates share the same x or y coordinate. Instead, you do the absolute value of the difference between the two distinct coordinates.
How do you calculate the midpoint of a line segment?
(x1+x2)/2, (y1+y2)/2
Where (x1, y1) and (x2, y2) are the coordinates of the endpoints
What is the equation of a circle centred at the point (a,b) with radius r?
(x-a)^2 + (y-b)^2 = r^2
What is the equation of a circle centred at the origin/point (0,0) with radius r?
x^2 + y^2 = r^2
Given two quadrilaterals with the same perimeter, which shape will always have the maximum area?
The square
