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The coordinates G(7, 3), H(9, 0), I(5, -1) form what type of polygon?

an obtuse triangle

1 Answer

5 votes

Answer:

Is an acute triangle

Explanation:

we have


G(7, 3),H(9, 0),I(5, -1)

so

The polygon is a triangle

we know that

the formula to calculate the distance between two points is equal to


d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}

Remember that

If applying the Pythagoras Theorem


c^(2)=a^(2)+b^(2) -----> is a right triangle


c^(2)>a^(2)+b^(2) -----> is an obtuse triangle


c^(2)<a^(2)+b^(2) -----> is an acute triangle

where

c is the greater side

step 1

Find the distance GH


G(7, 3),H(9, 0),I(5, -1)

substitute


d=\sqrt{(0-3)^(2)+(9-7)^(2)}


d=\sqrt{(-3)^(2)+(2)^(2)}


GH=√(13)\ units

step 2

Find the distance HI


G(7, 3),H(9, 0),I(5, -1)

substitute


d=\sqrt{(-1-0)^(2)+(5-9)^(2)}


d=\sqrt{(-1)^(2)+(-4)^(2)}


HI=√(17)\ units

step 3

Find the distance GI


G(7, 3),H(9, 0),I(5, -1)

substitute


d=\sqrt{(-1-3)^(2)+(5-7)^(2)}


d=\sqrt{(-4)^(2)+(-2)^(2)}


GI=√(20)\ units

step 4

Let


c=GI=√(20)\ units


a=HI=√(17)\ units


b=GH=√(13)\ units

Find
c^(2) ------>
c^(2)=(√(20))^(2)=20

Find
a^(2)+b^(2) ---->
(√(17))^(2)+(√(13))^(2)=30

Compare


20 < 30

therefore

Is an acute triangle

User RedScourge
by
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