CPM Homework Help : GC Problem 9-90

Jillian is trying to construct a square. She has started by constructing two perpendicular lines, as shown at right. If she wants each side of the square to have length $k$ , as shown below, describe how she should finish her construction.

Two perpendicular lines labeled, n, the vertical line, and, m, the horizontal line, intersect at point, P. A vertical line segment, k, is shown at the left.

Hint:

How can you use $k$ and the axes to create this square?

Answer:

Jillian should construct an arc centered at $P$ with a radius $k$ so that it intersects $n\text{ and }m$ each once (call these intersections $R$ and $S$ ). She should then make two more circles with radius $k$ , centered at $R$ and $S$ . The fourth vertex lies where these two circles intersect.