Without using pythagoras_ theoxem show that point A (4,4)
B (3,5) and c(-1,-1) are the vortices of a right angled
triangle
Answers
Answer:
ßTo show : Without using Pythagoras Theorem show that the points (4,4),(3,5) and (-1,-1) at the vertices of the right angle triangle ?
Solution :
If we show that line drawn by points is perpendicular then it form a right angle triangle.
If slope of two lines multiple is -1 then they are perpendicular.
Slope of the points A= (4,4), B= (3,5) and C=(-1,-1)
Slope formula,
m=\frac{y_2-y_1}{x_2-x_1}m=
x
2
−x
1
y
2
−y
1
Slope of AB, A= (4,4), B= (3,5)
m_1=\frac{5-4}{3-4}m
1
=
3−4
5−4
m_1=\frac{1}{-1}m
1
=
−1
1
m_1=-1m
1
=−1
Slope of BC, B= (3,5) and C=(-1,-1)
m_2=\frac{-1-5}{-1-3}m
2
=
−1−3
−1−5
m_2=\frac{-6}{-4}m
2
=
−4
−6
m_2=\frac{3}{2}m
2
=
2
3
Slope of AC, A= (4,4) and C=(-1,-1)
m_3=\frac{-1-4}{-1-4}m
3
=
−1−4
−1−4
m_3=\frac{-5}{-5}m
3
=
−5
−5
m_3=1m
3
=1
As m_1\times m_3=-1\times 1=-1m
1
×m
3
=−1×1=−1
So, AB is perpendicular to AC.
Therefore, ABC form a right angle triangle.
