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.
