Math Problem Statement
/
Solution
We are asked to find the endpoints of the median from vertex in triangle . From the image, we have the following details:
- The centroid of is at .
- The vertices of are:
Part A: Finding the median
The median from vertex will connect to the midpoint of side .
- Find the midpoint of side :
The midpoint formula for two points and is:
For and , the midpoint is:
So, the median starts at and ends at the midpoint .
Thus, the median begins at and ends at .
Would you like further details on the steps or concepts? Here are five related questions:
- How is the centroid of a triangle calculated?
- Why does the median always pass through the centroid of a triangle?
- How can you find the length of the median using the distance formula?
- What is the significance of the centroid dividing the medians into a 2:1 ratio?
- How can you find the equation of the line representing the median?
Tip: Remember that the centroid divides each median in a triangle into a 2:1 ratio, with the longer part being closer to the vertex.
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Math Problem Analysis
Mathematical Concepts
Geometry
Centroid of a Triangle
Midpoint Formula
Formulas
Midpoint Formula: ((x1 + x2) / 2, (y1 + y2) / 2)
Theorems
Centroid Theorem: The centroid of a triangle divides each median in a 2:1 ratio
Suitable Grade Level
Grades 9-10
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