Question

In question no. 19 if the point P moves in such a way that d(P, AB) ≥ maxi. {d(P, BC), d(P, CD), d(P, DA)}, then area of the region, representing all possible positions of the point P is equal to

• A. 2 sq. units
• B. 1 sq. units
• C. 6 sq. units
• D. 3 sq. units

Answer 1

Answer: (B)

1 sq. units

Answer 2

In this case, we must have, y ≥ x, x + y ≥ 6,

y ≥ 2. Shaded region represents the required area.

For A₁ : y = x = 6 – x

⇒ A₁ ≡ (3, 3), B_{1 ≡} (4, 4), C₁ ≡ (2, 4).

$\Delta _ { \mathrm { A } _ { 1 } \mathrm {~B} _ { 1 } \mathrm { C } _ { 1 } }$= − $\frac { 1 } { 2 }$ .2.1 = 1 sq. units.