CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Let a(P,OA)mind(P,AB),d(P,BC),d(P,OC) where d denotes the distance from the point to the corresponding line and S be the region consisting of all those points P inside the rectangle OABC such that O=(0,0),A=(3,0),B=(3,2)andC=(0,2), which satisfy the above relation, then area of the region S is

 
  1. 2 sq unit
  2. 3 sq unit
  3. 4 sq unit
  4. 1 sq unit


Solution

The correct option is A 2 sq unit
Let (x,y) be the coordinates of P'

Case 1: 0x1and0y1
min.d(P,AB),d(P,BC),d(P,OC)=d(P,OC)
d(P,OA)d(P,OC)
                        yx
Case 2: 1x2
min.d(P,AB),d(P,BC),d(P,OC)=d(P,BC)
d(P,OA)d(P,BC)
y3yory1
Case 3: 2x3 and 0y1
min.d(P,AB),d(P,BC),d(P,OC)=d(P,AB)
d(P,OA)d(P,AB)
y3xory3
Area of trapezium OAED ub required region
Area=12(3+1)×1=2squnit.

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image