show that the triangle formed by the points A(1,3),B(3,-1) and C(-5,-5) is a right angled triangle (by using slopes).
Answers
Answer:
True
Step-by-step explanation:
If triangle formed by A, B and C is a right angled triangle, AB should be perpendicular to BC.
This means: slope of AB = - 1 / slope of BC
Checking( for RHS = LHS )
Solving LHS:
⇒ slope of AB
⇒ ( - 1 - 3 ) / ( 3 - 1 )
⇒ - 4 / 2
⇒ - 2
Solving RHS:
⇒ - 1 / slope of BC
⇒ - 1 / [ ( - 5 + 1 ) / ( - 5 - 3 ) ]
⇒ - ( - 8 ) / ( - 4 )
⇒ 8 / ( - 4 )
⇒ - 2
As LHS = RHS triangle formed by these points is a right angled triangle.
Answer:
A (1,3) , B(3,-1) and C(-5,-5)
slope = (y2 - y1)/(x2 - X1)
AB slope = (-1-3)/(3-1) = -4/2 = -2
BC slope = (-5+1)/(-5-3) = -4/-8 = 1/2
AC slope = (-5-3)/(-5-1) = -8/-6 = 4/3
as we can see, slope of AB × slope of BC = 2×-1/2
= -1. hence AB is perpendicular to BC and the given ∆ is right angled ∆
[ product of the slopes of two perpendicular lines = -1 ]