
To calculate: The lengths of the medians of the triangle with the vertices

Answer to Problem 44E
The lengths of the medians of the triangle with vertices
Explanation of Solution
Given information:
The three vertices of the triangle
Formula used:
Median of a triangle is defined as the line segment joining two points from a vertex to the midpoint of the opposite side.
Mid-point formula between two points
Distance formula between two points
Calculation:
Consider the provided vertices of the triangle
Recall the mid-point formula between two points
Let D, E and F be the mid-points of line segments AB, BC and CA respectively.
So, mid-point of line segment
Now, mid-point of line segment
Mid-point of line segment
By plotting all the points on the coordinate plane, we get the following figure,
In the above figure, AE, BF and CD represents the three medians of the triangle ABC.
Recall the distance formula between two points
So, length of median AE is calculated as,
Length of median BF is calculated as,
Now, the length of median CD is calculated as,
Thus, the lengths of the medians of the triangle with vertices
Chapter 1 Solutions
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