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Questions and Answers
What is the midpoint of a line segment?
What is the formula to find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?
What is a property of the midpoint of a line segment?
What is an application of midpoints in computer graphics?
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What is the midpoint of the line segment with endpoints (3, 4) and (7, 10)?
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Study Notes
Midpoint
Definition
- The midpoint of a line segment is the point that divides the segment into two equal parts.
- It is the point that is equidistant from both endpoints of the segment.
Midpoint Formula
- The midpoint of a line segment with endpoints
(x1, y1)and(x2, y2)can be found using the formula:
M = ((x1 + x2) / 2, (y1 + y2) / 2)
- Where
Mis the midpoint.
Properties
- The midpoint is the average of the x-coordinates and the average of the y-coordinates of the endpoints.
- The midpoint is the point of symmetry for the line segment.
Example
- Find the midpoint of the line segment with endpoints
(3, 4)and(7, 10):
M = ((3 + 7) / 2, (4 + 10) / 2) = (5, 7)
Applications
- Midpoints are used in geometry to find the center of a triangle or a circle.
- Midpoints are used in engineering to find the center of gravity of an object.
- Midpoints are used in computer graphics to perform transformations and rotations.
Midpoint Definition
- Midpoint divides a line segment into two equal parts.
- It is equidistant from both endpoints of the segment.
Midpoint Formula
- Formula to find midpoint:
M = ((x1 + x2) / 2, (y1 + y2) / 2). -
Mrepresents the midpoint. -
x1andx2are x-coordinates of endpoints. -
y1andy2are y-coordinates of endpoints.
Midpoint Properties
- Midpoint is the average of x-coordinates and y-coordinates of endpoints.
- Midpoint is the point of symmetry for the line segment.
Example and Applications
- Example: Midpoint of
(3, 4)and(7, 10)is(5, 7). - Midpoints are used in geometry to find center of a triangle or a circle.
- Midpoints are used in engineering to find center of gravity of an object.
- Midpoints are used in computer graphics to perform transformations and rotations.
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Description
Learn about the definition and properties of midpoints in geometry, including the midpoint formula for finding the midpoint of a line segment.
