jmc

Question

Segment s_1 has endpoints at (3+2,5) and (4,7). Segment s_2 has endpoints at (6-2,3) and (3,5). Find the midpoint of the segment with endpoints at the midpoints of s_1 and s_2. Express your answer as (a,b).

Accepted Answer

Using the midpoint formula, we find that the midpoint of

s_{1}

has coordinates

(\frac{3 + 2 + 4}{2}, \frac{5 + 7}{2}) = (\frac{7 + 2}{2}, 6)

.

The midpoint of

s_{2}

has coordinates

(\frac{6 - 2 + 3}{2}, \frac{3 + 5}{2}) = (\frac{9 - 2}{2}, 4)

.

Applying the formula once more we see that the desired point is at

\frac{\frac{7 + 2 + 9 - 2}{2}}{2}, \frac{4 + 6}{2} = (4, 5) .