Joe and Marty are in the park playing catch. Tony joins them, and the boys want to stand so that the distance between any two of them is the same. Where do they stand? How do they figure this out precisely? What tool or tools could they use?

Modified from EngageNY ©Great Minds Disclaimer

Fill in the blanks below as each term is discussed:

The _______ between points *A* and *B* is the set consisting of *A*, *B*, and all points on the line *AB* between *A* and *B*.

Modified from EngageNY ©Great Minds Disclaimer

A ______ is a segment from the center of a circle to a point on the circle.

Given a point *C* in the plane and a number *r *> 0, the _______ with center *C* and radius *r* is the set of all points in the plane that are distance *r* from point *C*.

You need a compass and a straightedge.

Margie has three cats. She has heard that cats in a room position themselves at equal distances from one another and wants to test that theory. Margie notices that Simon, her tabby cat, is in the center of her bed (at S), while JoJo, her Siamese, is lying on her desk chair (at J). If the theory is true, where will she find Mack, her calico cat? Use the scale drawing of Margie’s room shown below, together with (only) a compass and straightedge. Place an M where Mack will be if the theory is true.

Draw your image on paper, take a picture, and upload it using the image upload icon .

If you do not have the ability to upload an image of your work type "Image is on paper."

Modified from EngageNY ©Great Minds Disclaimer