About Cynthia Watanabe Expertise I have taught high school mathematics for fourteen years. I can help students develop proofs, solve problems which require some algebra skills. Some topics that you may wish to explore include points, lines, planes, segments, rays, angles, polygons, solids, measurement, area, and volume.
Experience I have taught high school mathematics fourteen years.
Education/Credentials B.S. Secondary Education with a concentration in Mathematics. Master of Library and Information Science with a concentration in Archiving.
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Your question was
"PQRS is a rectangle with PQ twice as long as QR. T is the midpoint of
RS. TQ is drawn. Sketch the locus of the midpoints of segments that are
parallel to TQ and end on the sides of the rectangle.
What exactly does this mean, and how do I solve it?"
The length of the rectangle should be twice as long as the width. You will want to measure this with your ruler.
TQ is in Green.
Measure TQ with your ruler and draw the midpoint.
Now, the red lines are connecting QR and RT. Measure each "Red" line and draw the midpoint.
Now,the bluish lines connect PQ and TS. Measure each "Blue" line and draw the midpoint.
Now, the orange lines are connecting QR and TS. Measure each "Orange" line and draw the midpoint.
What do you notice?
There is a theorem that says the locus of points equidistant from 2 points is the perpendicular bisector of the segment they define.
This works for your diagram BUT....the red, blue, and orange lines will give you different perpendicular bisectors because they are connecting different sides of the rectangle.
Let me know if you have any more questions. Take care, Cynthia
