Math Problem Statement
Find the coordinates of the points which divide the line segment joining points (-2,2) and (0,8) in four equal parts
Solution
To find the coordinates of the points that divide the line segment joining the points and into four equal parts, we can follow these steps:
Step 1: Calculate the total length of the line segment
The line segment is divided into four equal parts, so we will first find the total vector from point to point .
Step 2: Determine the vector and intervals
The vector from to is:
Since we need to divide this segment into four equal parts, the ratio for each segment will be and .
Step 3: Calculate the coordinates of the dividing points
The points , , and will divide the line segment into four equal parts.
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Point divides the line segment in the ratio :
The coordinates of are given by the section formula:
For and :
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Point divides the line segment in the ratio :
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Point divides the line segment in the ratio :
Final Answer:
The coordinates of the points that divide the line segment into four equal parts are:
Would you like more details or have any further questions?
Here are 5 related questions to consider:
- How can you find the ratio in which a line segment is divided by a given point?
- What are the coordinates of the midpoint of a line segment with endpoints and ?
- How do you calculate the area of a triangle formed by three points in the coordinate plane?
- How can you find the equation of the line passing through two given points?
- What is the distance between two points in 3-dimensional space?
Tip: When dividing a line segment into multiple equal parts, use the section formula with appropriate ratios to find the precise coordinates of each dividing point.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Section Formula
Formulas
Section Formula
Theorems
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Suitable Grade Level
High School
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