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Determine the vertices of a triangle whose sides have the midpoints (1, 0), (2, -1), and (3, 1).
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
Since the midpoints of the sides of a triangles are given in the problem, then we need to use midpoint formula of two points as follows
For the line segment AB:
For the line segment BC:
For the line segment AC:
From the set of linear equations:
By elimination method, solve for the values of x1, x2, and x3.
Subtract (3) from (1), we have
Add (5) and (7), we have
Substitute the value of x1 to (1)
Substitute the value of x1 to (5)
From the set of linear equations:
By elimination method, solve for the values of y1, y2, and y3.
Subtract (4) from (2), we have
Substitute (6) to (8), we have
Substitute the value of y1 to (2)
Substitute the value of y1 to (6)
Therefore, the vertices of a triangle are
