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Geocaching with Jack and Anna

Topic:
Geometry

Jack

Jack

Jack buried a Matchbox car in the schoolyard as part of his geocaching club. He remembers hiding the car ⅓ of the way between the back door and the big oak tree. The location of the back door is point B(0,3), and the location of the big oak tree is point T(12,3).

1. Determine the location of the car and label this point as M. What are the coordinates of point M?

Anna

Anna

2. Jack’s sister, Anna, also hid something for the geocaching club.  She remembers burying a My Little Pony figurine (Rarity) between the fence and the rose bush. The location of the fence is point P(1,2), and the location of the rose bush is point R(16,14).

a. Suppose Anna buried the My Little Pony halfway between the fence and the rose bush. What would be the coordinates of the My Little Pony? How do you know?

b. Suppose Anna buried a friendship bracelet one-fourth of the way between the fence and the rose bush. What would be the coordinates of the bracelet? How do you know?