Question

Assertion (A): Area of the triangle formed by the points $z,iz,z+iz$ where $z=6+8i$ is $50$ sq.units.
Reason(R): Area of triangle formed by $z,iz,z+iz$ is $\frac{1}{2}|z{|}^2$.

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true and R is not the correct explanation of A
• C. A is false, R is true
• D. A is true R is false

Answer 1

The correct option is A Both A and R are true and R is the correct explanation of A

Hence vertices are
$z_1=6+8i$
$z_2=-8+6i,$
$z_3=-2+14i$
$z_1-z_2=14+2i=a$
$z_2-z_3=-6-8i=b$
$z_3-z_1=-8+6i=c$
$|c|=|-8+6i|=10$
$|a|=|14+2i|=10\sqrt{2}$
$|b|=|-6-8i|=10$
Thus the area of the triangle formed is a right angled triangle will be
$\frac{1}{2}|z{|}^2$
$=\frac{1}{2}\left(100\right)$
$=50$ sq units.
Hence, option 'A' is correct.