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Question

Let A(0,1),B(1,1),C(1,1) and D(1,0) be four points. If P is any other point, then the minimum value of PA+PB+PC+PD is equal to

A
5
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B
25
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C
35
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D
45
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Solution

The correct option is B 25
We need PA+PB+PC+PD to be minimum
Let's form a triangle using any two coordinates out of 4 say A and C and third vertex as P
In ΔPAC
PA+PCAC ...(1)
then taking coordinates B and D
In ΔPBD
PB+PDBD ...(2)
Adding (1) and (2) we get
PA+PB+PC+PDAC+BD ...(3)

min value of PA+PB+PC+PD=AC+BD
AC=(10)2+(11)2=5
BD=(11)2+(01)2=5
AC+BD=25
min value of PA+PB+PC+PD=25

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