Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Matrices

Olympiad workbook · IOQM · Matrices

Let P_0=(3,1) and define P_ n+1 = (x_ n , y_ n ) for n ≥ 0 by x_...

Let P0=(3,1)anddefine\mathrm{P}_0=(3,1) and define\mathrm{P}_{\mathrm{n}+1}=(xn,yn)\left(\mathrm{x}_{\mathrm{n}}, \mathrm{y}_{\mathrm{n}}\right) for n≥0\mathrm{n} \geq 0 by xn+1=−3xn−yn2,yn+1=−xn+yn2x_{n+1}=-\frac{3 x_n-y_n}{2}, y_{n+1}=-\frac{x_n+y_n}{2} Find the area of the quadrilateral formed by the points P96,P97,P98,P99\mathrm{P}_{96}, \mathrm{P}_{97}, \mathrm{P}_{98}, \mathrm{P}_{99}.

Correct answer

8

Step-by-step solution

P≡(3,1)P1≡(−4,−2)P2≡(5,3)P3≡(−6,−4)\begin{aligned} & \mathrm{P} \equiv(3,1) \\ & \mathrm{P}_1 \equiv(-4,-2) \\ & \mathrm{P}_2 \equiv(5,3) \\ & \mathrm{P}_3 \equiv(-6,-4) \end{aligned} from shifting  area =12∣35−4−6313−2−41∣12(9−5−10+12+16−12−6+12)=8 Ans. \begin{aligned} \text { area } & =\frac{1}{2}\left|\begin{array}{llll} 3 & 5 & -4 & -63 \\ 1 & 3 & -2 & -41 \end{array}\right| \\ & \frac{1}{2}(9-5-10+12+16-12-6+12) \\ & =8 \text { Ans. } \end{aligned}
Practice Matrices on Quantrex Academy →

More from Matrices

Let P_0=(3,1) and define P_ n+1 =(x_ n , y_ n ) for n ≥ 0 by x_ n+1 =-(3 x_n-y_n)/(2), y_… Olympiad workbook Full Matrices list All Olympiad workbook PYQs