Question

your own
wesley designs a shark fin for a costume. he chooses
the points k(1, 7), l(3, 5), m(6, -3), n(-5, -2), and
p(-1, 1) to model the fin.
a. graph the points on the coordinate plane.
b. connect the points in order from k to l to m to n
to p, and back to k.
c. how many sides does the polygon that you drew
have? classify the polygon by the number of sides.
construct arguments for problems 3–4, tell whether
the figure is a polygon. if it is a polygon, give the number
of sides and classify it. if it is not, explain why not.
3.
4.

Explanation:

For the Wesley's shark fin problem (parts A, B, C):

Step1: Count distinct vertices

The points are $K(1, 7)$, $L(3, 5)$, $M(6, -3)$, $N(-5, -2)$, $P(-1, 1)$: 5 unique points.

Step2: Classify by side count

A polygon with 5 sides is a pentagon.

This figure is a closed shape made of only straight line segments, with no curved sides or intersecting edges, so it is a polygon. Counting the straight sides gives 6 total.

A polygon is defined as a closed figure with only straight line segments as sides. This figure has a curved edge, so it does not meet the definition of a polygon.

Answer:

A. (Graph: Plot each point on a coordinate plane: $K$ at (1,7), $L$ at (3,5), $M$ at (6,-3), $N$ at (-5,-2), $P$ at (-1,1))
B. (Connect the points in the given sequential order: $K \to L \to M \to N \to P \to K$)
C. The polygon has 5 sides. It is a pentagon.

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For Problem 3: