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Questions and Answers
What is the distance formula?
What is the distance formula?
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
What is the midpoint formula?
What is the midpoint formula?
(x₁+x₂)/2, (y₁+y₂)/2
What is the equation of a circle?
What is the equation of a circle?
(x-h)²+(y-k)²=r²
How do you identify the center of the circle from the equation (x-3)²+(y+8)²=9?
How do you identify the center of the circle from the equation (x-3)²+(y+8)²=9?
How do you identify the radius of the circle from the equation (x-3)²+(y+8)²=9?
How do you identify the radius of the circle from the equation (x-3)²+(y+8)²=9?
If two pairs have the same X but different Y, then it is a function.
If two pairs have the same X but different Y, then it is a function.
What is the vertical line test?
What is the vertical line test?
How do you find the domain and range of a graph?
How do you find the domain and range of a graph?
What is the equation for a linear function?
What is the equation for a linear function?
What is the slope equation?
What is the slope equation?
What is the point-slope form?
What is the point-slope form?
Vertical lines are parallel.
Vertical lines are parallel.
Horizontal lines and vertical lines are opposite.
Horizontal lines and vertical lines are opposite.
What is the perpendicular line formula?
What is the perpendicular line formula?
If the slopes are not the same or -1, then the lines are either parallel or perpendicular.
If the slopes are not the same or -1, then the lines are either parallel or perpendicular.
What formula do you use to find if a line is parallel or perpendicular through the point (x,y)?
What formula do you use to find if a line is parallel or perpendicular through the point (x,y)?
What is a coordinate system?
What is a coordinate system?
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Study Notes
Distance and Midpoint Formulas
- Distance Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²] calculates the distance between two points in a coordinate plane.
- Midpoint Formula: Find the midpoint between two points using (x₁ + x₂)/2, (y₁ + y₂)/2.
Circle Equations
- Equation of a Circle: The general form is (x-h)² + (y-k)² = r², where (h, k) is the center and r is the radius.
- Center Identification: For example, in (x-3)² + (y+8)² = 9, the center is at (3, -8).
- Radius Identification: From the equation (x-3)² + (y+8)² = 9, the radius r is derived from r² = 9, resulting in r = 3.
Functions and Relations
- A function requires each domain member to have exactly one corresponding range member. Two pairs, like (9,5) and (9,-5), share the same x-value but differ in y-values, indicating it's not a function.
- Vertical Line Test: A function's graph passes this test if any vertical line crosses it at only one point.
Domain and Range
- Domain: Refers to the set of possible x-values (horizontal).
- Range: Refers to the set of possible y-values (vertical).
- Use parentheses for open intervals, brackets for closed intervals, and infinity symbols when relevant.
Linear Functions
- Linear Function Equation: y = mx + b, where m is the slope and b is the y-intercept.
- Slope Equation: Calculated as (y₂ - y₁) / (x₂ - x₁) to determine the steepness of the line.
- Point-Slope Form: Expressed as y - y₁ = m(x - x₁), useful for writing equations from a point and slope.
Line Properties
- Vertical Lines: Have the same slope and are parallel.
- Horizontal Lines: Perpendicular to vertical lines, with slopes of -1.
- Perpendicular Line Formula: For two lines, m₁ * m₂ = -1 indicates that they are perpendicular.
Determining Relationships Between Lines
- Lines that are not parallel or perpendicular do not share the same slope or a negative reciprocal relationship.
- Use y - y₁ = m(x - x₁) to find if a line through a given point is parallel or perpendicular to another line.
Coordinate System
- A grid featuring intersecting lines that help locate points and features in a two-dimensional space.
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