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Lemur [1.5K]
3 years ago
12

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

Mathematics
2 answers:
chubhunter [2.5K]3 years ago
7 0

Answer:

ACUTE !!!!!!!!

Step-by-step explanation:

Marrrta [24]3 years ago
6 0

Answer:

Is an acute triangle

Step-by-step explanation:

we know that

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

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

we have

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

step 1

Find the distance GH

substitute in the formula

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

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

GH=\sqrt{13}\ units

step 2

Find the distance IH

substitute in the formula

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

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

IH=\sqrt{17}\ units

step 3

Find the distance GI

substitute in the formula

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

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

GI=\sqrt{20}\ units

step 4

Verify what type of triangle is the polygon

we know 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

we have

c=\sqrt{20}\ units

a=\sqrt{17}\ units

b=\sqrt{13}\ units

substitute

c^{2}= (\sqrt{20})^{2}=20

a^{2}+b^{2}=(\sqrt{17})^{2}+(\sqrt{13})^{2}=30

therefore

c^{2}< a^{2}+b^{2}

Is an acute triangle

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