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 Margies room shown below, together with only a compass and straightedge. Place M where Mack will be if the theory is true.

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Explanation:

J = Jojo's position (desk)

S = Simon's position (bed)

Place the non-pencil part of the compass at the center of the bed. Extend the compass so that its width reaches from the bed to the desk. Draw an arc. Keeping the same compass width, place the non-pencil end at the desk and draw another arc.

See the diagram below.

The two arcs intersect at two points A and B. Line AB is formed that is the perpendicular bisector of segment JS. Point J is at the desk and point S is at the bed.

Any point on line AB is equidistant from points J and S. If M is on line AB, then segments MJ and MS are the same length. Note how line AB falls close to the bookcase and the rug. So Mack could be on those two items.

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step-by-step explanation:

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225