Complex NumbersHard
Question
If a, b, c and u, v, w are the complex numbers representing the vertices of two triangles such that c = (1 - r) a + rb and w = (1 - r) u + rv, where r is a complex number, the the two triangles
Options
A.have the same area
B.are similar
C.are conguent
D.None of these
Solution
Since a, b, c and u, v, w are the vertices of two triangles.
Also, c = (1- r)a + rb and w = (1- r)u + rv .........(i)
Consider
Applying R3 → R3 -{(1-r)R1 + rR2}
[form Eq. (i)]
= 0
Hence, two triangles are similar.
Also, c = (1- r)a + rb and w = (1- r)u + rv .........(i)
Consider
Applying R3 → R3 -{(1-r)R1 + rR2}
[form Eq. (i)]= 0
Hence, two triangles are similar.
Create a free account to view solution
View Solution FreeMore Complex Numbers Questions
If represents a pair of intersecting lines with angle of intersection ′θ′ then the value of |A| is...If centre of square ABCD is at z = 0. If affix of vertex A is z1, centroid of triangle ABC is/are -...If 1, α1, α2, α3, .....α8, are nine, ninth roots of unity (taken in counter-clockwise sequence) then...is equal to -...If −3 + ix2y is the conjugate of x2 + y + 4i, then real values of x and y are-...