Points , and are the midpoints of the sides of triangle . Find the coordinates of the points , and . (Labels , and are arbitrarily assigned to coordinates).

Source: NCTM Mathematics Teacher 2008

**SOLUTION
**

Draw a first line passing through and parallel to . Equation of the first line

Slope of

Draw a second line passing through point Z and parallel to . Equation of the second line

Substitute the values of into the equation

Equation of the second line

The two lines intersect at point the coordinates of which satisfy both Eq. and .

Solving for yields

Coordinates of vertex .

Suppose is the midpoint of side . The midpoint formula yields the coordinates of vertex

Coordinates of vertex .

Similarly is the midpoint of side . In this case the midpoint formula yields the coordinates of

Coordinates of vertex .

**Answer**: