Transformations
This transformation moves every point the same distance in the same direction.
What is a translation?
All points on a circle are this distance from the center.
What is the radius?
Two lines with slopes m₁ and m₂ are perpendicular when their slopes have this relationship.
What is opposite reciprocal slopes?
To prove two segments are congruent using coordinates, we show they have this.
What is the same length/distance?
The transformation (x,y) → (y,-x) represents this type of movement around the origin.
What is a 90° clockwise rotation?
The equation (x-h)² + (y-k)² = r² represents a circle with this point as its center.
What is (h,k)?
The point-slope form of a line through (x₁,y₁) with slope m is this equation.
What is y - y₁ = m(x - x₁)?
This formula finds the distance between any two points in the coordinate plane.
What is Pythagorean Theorem/Distance Formula?
This transformation takes points in the plane as inputs and gives other points as outputs, just like this type of mathematical relationship.
What is a function?
A parabola is the set of all points equidistant from this point and this line.
What are the focus and directrix?
Two parallel lines must have this relationship between their slopes.
What is they are equal/the same?
To prove a quadrilateral is a rectangle, we must show all angles are this and all sides are congruent.
What is 90 degrees/right angles? WITH OPPOSITE RECIPROCAL SLOPES AS OUR EVIDENCE!
When point A(2,3) is reflected across the y-axis, its image has these coordinates.
What is A'(-2,3)?
The Pythagorean Theorem helps derive this equation for a circle centered at the origin.
What is x² + y² = r²?
A line with slope 2 passing through (1,3) will also pass through this point.
What is (3,7)?
The midpoint formula shows this point divides a segment into two equal parts.
What is ((x₁+x₂)/2, (y₁+y₂)/2)?
This type of transformation preserves distance and angle measures, unlike a dilation.
What is a rigid motion/isometry?
When a circle's equation is x² + y² + 6x - 8y + 25 = 0, its center is at this point.
What is (-3,4)?
The perpendicular bisector of segment AB is the set of all points with this property.
What is equidistant from points A and B?
To prove triangles are similar using coordinates, we must show corresponding angles are equal and sides have this.
What are proportional lengths?