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Mathematics Question on Applications of Determinants and Matrices

The area of triangle with vertices (K,0),(4,0),(0,2){(K, 0),(4,0) , (0, 2)} is 44 square units, then value of KK is

A

0 or 8{0 \, or \, 8}

B

0 or −8{0 \, or \, - 8}

C

0{0}

D

8{ 8}

Answer

0 or 8{0 \, or \, 8}

Explanation

Solution

Let A(K,0),B(4,0),C(0,2)A(K, 0), B(4,0), C(0,2)
Now, we have
ar (Δ ABC)=4(\Delta \,A B C)=4
∴12∣K(0−2)+4(2−0)+0(0−0)∣=4\therefore \frac{1}{2}|K(0-2)+4(2-0)+0(0-0)|=4
⇒ 12∣−2K+8∣=4\Rightarrow\, \frac{1}{2}|-2 K+8|=4
⇒ ∣−2K+8∣=8\Rightarrow \, |-2 K+8|=8
⇒−2K+8=±8\Rightarrow -2 K+8=\pm 8
⇒−2K=±8−8\Rightarrow -2 K=\pm 8-8
⇒−2K=0\Rightarrow -2 K=0 or 16
⇒ K=0\Rightarrow \, K =0 or 8