Question

Let z₁, z₂ and z₃ be three distinct points in the complex plane such that the segment joining z₁ and z₂ is perpendicular to the segment joining z₁ and z₂. If |z₁-z₂|=5 and|z₁-z₃|=12 then|z₂-z₃| is equal to

• A. 17
• B. 7
• C. 13
• D. 14
• E. 9

Answer 1

The Correct Option is C

We are given three distinct points \(z_1, z_2, z_3\) in the complex plane such that:

• The segment joining \(z_1\) and \(z_2\) is perpendicular to the segment joining \(z_1\) and \(z_3\).
• \(|z_1 - z_2| = 5\) and \(|z_1 - z_3| = 12\).

We need to find \(|z_2 - z_3|\). 

Since the segment joining \(z_1\) and \(z_2\) is perpendicular to the segment joining \(z_1\) and \(z_3\), we can apply the Pythagorean theorem in the right triangle formed by the points \(z_1 \), \( z_2 \), \( z_3\).

According to the Pythagorean theorem:

\(|z_2 - z_3|^2 = |z_1 - z_2|^2 + |z_1 - z_3|^2\)

Substituting the given values:

\(|z_2 - z_3|^2 = 5^2 + 12^2 = 25 + 144 = 169\)

\(|z_2 - z_3| = \sqrt{169} = 13\)

The answer is 13.