Transformation Rules and Equations of Line
What transformation moves a figure up, down, left or right without changing its size, shape or orientation?
Translation
example: (x,y) --> (x +1), (y-2)
move right add to x, move left subtract from x
move up add to y, move left subtract from y
What form of a line is written as y=mx+b?
slope-intercept form
What is the standard form equation of a circle centered at (h,k)?
(x−h)2 + (y−k)2 = r2
What formula finds the distance between two points?
distance formula
Two angles that add up to 180° are called what?
Supplementary
Which transformation produces a mirror image of a figure across a line, such that the figure keeps its size but changes orientation?
Reflection
x-axis (x,y) --> (x, -y)
y-axis (x,y) --> (-x, y)\
line x=y --> (y,x)
In slope‑intercept form, what does m represent?
Slope
When should you use the equation of a circle instead of circumference or area formulas?
When you are given or asked to find coordinates, a center, a radius, or to identify points on a circle in the coordinate plane.
What formula finds the midpoint of a segment?
Midpoint Formula
Two angles that add up to 90° are called what?
Complementary
What is the rule for a 90° counterclockwise rotation about the origin?
(x,y) --> (-y, x)
note: 90° counterclockwise and 270° clockwise rotate will have the image land in the same position.
What form is written as y − y1 = m(x−x1)?
Point-slope form
What formula is used to find the arc length of a circle?
Arc Length=(2 * pi * radius) * x/360 degrees.
In slope, what does “rise” mean?
Change in y
When two lines intersect, the opposite angles are called what?
Vertical angles
What is the rule for a 180° rotation?
(x,y) = (-x, -y)
What form is written as Ax + By = C?
Standard Form
When do you use the arc length formula instead of the circumference formula?
When finding the distance along the outside of a circle, but only part of the circle, using a central angle.
What slope means a line is vertical?
Undefined
Same‑side interior angles on parallel lines add up to what?
180 degrees
What term describes transformations that preserve distance and angle measure, keeping figures congruent to the original?
Rigid Motion
Which form always has x and y on the same side of the equation?
Standard Form
What formula is used to find the sector of a circle?
Sector area is pi *radius2 * x/360 degrees.
What slope means a line is horizonal?
y = 0
What is the sum of all the angles in a triangle equal? What is the name of the theorem?
180 degrees. This is known as the Triangle Sum Theorem