rich4335
Answered

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Could the points (-4,3), (-1,1) and (1,3) form the vertices of a right triangle? Why or why not?

Sagot :

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[tex]A=(-4,3),B=(-1,1),C=(1,3)\\ |AB|=\sqrt{(-4+1)^2+(3-1)^2}=\sqrt{9+4}=\sqrt{13}\\ |BC|=\sqrt{(-1-1)^2+(1-3)^2}=\sqrt{4+4}=\sqrt{8}\\ |AC|=\sqrt{(-4-1)^2+(3-3)^2}=\sqrt{25+0}=5\\ L=\sqrt{13}^2+\sqrt{8}^2=13+8=21\neq5^2\neq\ R[/tex]

It's impossible to form right triangle using thes points.

Answer:

The given points of triangle do not form a right triangle because they are satisfying the property of right angle triangle.

Step-by-step explanation:

Given : The points (-4,3), (-1,1) and (1,3)

To find : Could the points form the vertices of a right triangle? Why or why not?

Solution :

First we find the distance between the points so that we get the length of the sides.

Let, A=(-4,3), B=(-1,1), C=(1,3)

Distance formula is

[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

The distance between point A and B

[tex]|AB|=\sqrt{(-4+1)^2+(3-1)^2}=\sqrt{9+4}=\sqrt{13}[/tex]

The distance between point B and C

[tex]|BC|=\sqrt{(-1-1)^2+(1-3)^2}=\sqrt{4+4}=\sqrt{8}[/tex]

The distance between point A and C

[tex]|AC|=\sqrt{(-4-1)^2+(3-3)^2}=\sqrt{25+0}=5[/tex]

According to property of triangle,

If the square of larger side of triangle is equating to the sum of square of smaller side  [tex]a^2=b^2+c^2[/tex] the triangle is right triangle .

Larger side of the triangle is AC=5 unit and smaller sides are [tex]AB=\sqrt{13}[/tex] and [tex]BC=\sqrt{8}[/tex]

[tex]AC^2=AB^2+BC^2[/tex]

[tex]5^2=\sqrt{13}^2+\sqrt{8}^2[/tex]

[tex]25=13+8[/tex]

[tex]25\neq21[/tex]

So, The given points or the vertices of triangle do not form a right triangle because they are satisfying the property of right angle triangle.

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