Question

If A(3 + 4i), B(– 4 + 3i) and C(4 + 3i) be the vertices of

DABC and altitude AD intersects the circumcircle of the DABC at the point D, then affix of the point D is –

• A. – 3 + 4i
• B. 3 – 10i
• C. 3 – 4i
• D. – 3 – 4i

Answer 1

Answer: (C)

3 – 4i

Answer 2

Sol. Since A, B and C lie on a circle with centre at origin and centroid G is (1, 10/3)

\ The orthocentre H is (3, 10)

equation of the line BC is y – 3 = 0

Since D is the image of H in BC

\ coordinate of D are given by

$\frac{x - 3}{0} = \frac{y - 10}{1} = - 2.\frac{10 - 3}{1} = - 14$

\ affix of D is 3 – 4i.