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Kisachek [45]
3 years ago
5

The coordinates A(2, 1), B(7, 1), C(2, 4) form what type of polygon?

Mathematics
2 answers:
MAVERICK [17]3 years ago
4 0

Answer:  The correct option is (C) a right triangle.

Step-by-step explanation:  The given co-ordinates of a polygon are A(2, 1), B(7, 1), C(2, 4).

We are to select the correct type of the polygon.

Since we have the co-ordinates of the three points A, B and C, so the polygon will surely be a triangle.

Now, the lengths of the three sides AB, BC and CA of ΔABC can be calculated using distance formula as follows :

AB=\sqrt{(7-2)^2+(1-1)^2}=\sqrt{25+0}=\sqrt{25}=5,\\\\BC=\sqrt{(2-7)^2+(4-1)^2}=\sqrt{25+9}=\sqrt{34},\\\\CA=\sqrt{(2-2)^2+(1-4)^2}=\sqrt{0+9}=\sqrt{9}=3.

We have

AB^2+CA^2=5^2+3^2=25+9=34,\\\\BC^2=(\sqrt{34})^2=34.

This implies that

AB^2+CA^2=BC^2,

which is the Pythagorean triple. Hence, triangle ABC is a right-angled triangle.

Thus, (C) is the correct option.

Vesnalui [34]3 years ago
3 0
It appears to be a right triangle.
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