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Mathematics

The coordinate grid below shows Alice’s neighborhood. Point A represents Alice’s house. Her friends Barbara, Carlos, and Dana also live in the neighborhood.

y

8 7 6 5 4 3 2 1

# A

0

1

2345678

x

Part A Plot Point A on the grid in your answer booklet. Barbara’s house is at the point (1, 5). Plot that point and label it Point B. Carlos’ house is at the point (1, 2). Plot that point and label it Point C.

Part B If Alice walks to Barbara’s house and the two girls then walk to Carlos’ house before returning to Alice’s, which type of triangle is formed?

Part C Point D represents Dana’s house. When the four houses are connected by line segments, they form a trapezoid.

Find and label a Point D on the grid. Identify the coordinates of the point you labeled as Point D and explain why quadrilateral ABCD is a trapezoid.

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