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 z = 1 + i, then multiplicative inverse of z2 is -...Let z and w be two complex number such that |z| ≤ 1, |w|1 and |z + iw| = |z - | = 2, then z equals...Which of the following complex numbers lies along the angle bisectors of the line -L1 : z = ( 1 + 3λ) + i(1 + 4_...The equation ||z + i| - |z - i|| = k represents...The number of solutions of the system of equations Re(z2) = 0, | z | = 2 is -...