Math Problem Statement
Question 4. Triangle ABC has vertices A(10, 2), B(4, −2), and C(−4, 6). Determine the equation of the median from the vertex A.
Solution
To determine the equation of the median from vertex of triangle , follow these steps:
Step 1: Find the midpoint of side .
The median from vertex will pass through the midpoint of the opposite side . The coordinates of the midpoint of a line segment with endpoints and can be found using the midpoint formula:
For points and , the coordinates of the midpoint are:
So, the midpoint of side is .
Step 2: Determine the equation of the line passing through and .
The equation of a line passing through two points and can be written in the point-slope form:
where is the slope of the line, given by:
For the points and :
Since the slope , the line is horizontal. The equation of a horizontal line through the point (or any point on the line) is simply:
Final Answer:
The equation of the median from vertex of triangle is:
Would you like more details or have any questions? Here are some related questions you might consider:
- How do you find the equation of a median when the vertices have different y-coordinates?
- What is the significance of the median in a triangle?
- How can you find the centroid of a triangle using the medians?
- How would the equation of the median change if point had different coordinates?
- How do you find the equation of a median in 3D space?
Tip: When working with triangles, always double-check your midpoint calculations, as this can affect the equation of the median.
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Math Problem Analysis
Mathematical Concepts
Geometry
Coordinate Geometry
Midpoint Formula
Equation of a Line
Formulas
Midpoint formula
Point-slope form of a line equation
Theorems
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Suitable Grade Level
Grades 9-12
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