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Questions and Answers
What is the formula used to find the midpoint of a line segment?
In which quadrant would the point (-3, 5) be located?
What is the coordinate plane divided into?
What is the formula used to calculate the distance between two points on a coordinate plane?
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What is the Pythagorean Theorem formula?
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What is the purpose of the midpoint formula?
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What is the coordinate plane used for?
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What is the term for the vertical axis on a coordinate plane?
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What is the minimum value that the distance formula can yield?
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What is the point of intersection of the x-axis and y-axis in a coordinate plane?
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Which of the following is a characteristic of the midpoint of a line segment?
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What is the main focus of coordinate geometry?
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What is the purpose of the distance formula in coordinate geometry?
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In which quadrant would the point (3, -4) be located?
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What is the result of calculating the distance between two points with the same coordinates?
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Study Notes
Distance Formula
Definition
The distance formula is a mathematical formula used to calculate the distance between two points in a coordinate plane.
Formula
The distance formula is:
√((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Midpoint Formula
Definition
The midpoint formula is used to find the midpoint of a line segment.
Formula
The midpoint formula is:
((x1 + x2)/2, (y1 + y2)/2)
where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment.
Graphing On The Coordinate Plane
Quadrants
- The coordinate plane is divided into four quadrants:
- Quadrant I: x > 0, y > 0
- Quadrant II: x < 0, y > 0
- Quadrant III: x < 0, y < 0
- Quadrant IV: x > 0, y < 0
Plotting Points
- To plot a point, identify the x-coordinate (left/right) and y-coordinate (up/down) and mark the intersection.
Coordinate Geometry
Coordinate Plane
- A coordinate plane is a two-dimensional plane with a horizontal x-axis and a vertical y-axis.
- Each point on the plane is identified by an ordered pair (x, y).
Coordinate Geometry Formulas
- Distance Formula: √((x2 - x1)^2 + (y2 - y1)^2)
- Midpoint Formula: ((x1 + x2)/2, (y1 + y2)/2)
Pythagorean Theorem
Definition
The Pythagorean Theorem is a mathematical concept that describes the relationship between the lengths of the sides of a right-angled triangle.
Formula
The Pythagorean Theorem formula is:
a^2 + b^2 = c^2
where a and b are the lengths of the legs of the right triangle, and c is the length of the hypotenuse.
Distance Formula
- Calculates the distance between two points in a coordinate plane.
- Formula: √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Midpoint Formula
- Finds the midpoint of a line segment.
- Formula: ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of the two endpoints.
Graphing On The Coordinate Plane
Quadrants
- The coordinate plane is divided into four quadrants.
- Quadrant I: x > 0, y > 0.
- Quadrant II: x < 0, y > 0.
- Quadrant III: x < 0, y < 0.
- Quadrant IV: x > 0, y < 0.
Plotting Points
- To plot a point, identify the x-coordinate (left/right) and y-coordinate (up/down) and mark the intersection.
Coordinate Geometry
Coordinate Plane
- A coordinate plane is a two-dimensional plane with a horizontal x-axis and a vertical y-axis.
- Each point on the plane is identified by an ordered pair (x, y).
Coordinate Geometry Formulas
- Distance Formula: √((x2 - x1)^2 + (y2 - y1)^2).
- Midpoint Formula: ((x1 + x2)/2, (y1 + y2)/2).
Pythagorean Theorem
- Describes the relationship between the lengths of the sides of a right-angled triangle.
- Formula: a^2 + b^2 = c^2, where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Distance Formula
- Calculates the distance between two points (x1, y1) and (x2, y2) in a coordinate plane
- Formula: √((x2 - x1)^2 + (y2 - y1)^2)
- Always yields a positive value or zero
Graphing Points
- Ordered pairs (x, y) represent points in a coordinate plane
- x-axis is the horizontal axis, and y-axis is the vertical axis
- Origin is the point where the x-axis and y-axis intersect, represented by (0, 0)
- Four quadrants:
- I: x > 0, y > 0
- II: x < 0, y > 0
- III: x < 0, y < 0
- IV: x > 0, y < 0
Midpoint Formula
- Calculates the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)
- Formula: ((x1 + x2)/2, (y1 + y2)/2)
- Midpoint is equidistant from the two endpoints
Coordinate Geometry
- Studies geometric shapes and properties using coordinates
- Includes points, lines, line segments, rays, and angles
- Used to:
- Calculate distances and midpoints
- Find slopes and equations of lines
- Identify and graph geometric shapes
- Solve geometric transformation problems
Studying That Suits You
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Description
Test your knowledge of important formulas in coordinate geometry, including the distance formula and midpoint formula.
