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
\(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)
The distance between point A and B
\(|AB|=\sqrt{(-4+1)^2+(3-1)^2}=\sqrt{9+4}=\sqrt{13}\)
The distance between point B and C
\(|BC|=\sqrt{(-1-1)^2+(1-3)^2}=\sqrt{4+4}=\sqrt{8}\)
The distance between point A and C
\(|AC|=\sqrt{(-4-1)^2+(3-3)^2}=\sqrt{25+0}=5\)
According to property of triangle,
If the square of larger side of triangle is equating to the sum of square of smaller side \(a^2=b^2+c^2\) the triangle is right triangle .
Larger side of the triangle is AC=5 unit and smaller sides are \(AB=\sqrt{13}\) and \(BC=\sqrt{8}\)
\(AC^2=AB^2+BC^2\)
\(5^2=\sqrt{13}^2+\sqrt{8}^2\)
\(25=13+8\)
\(25
eq21\)
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.
