# if z satisfy mod{z-3i} + mod{z-4} = 5 then minimum value of mod{z}

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## 1 Answers

AKASH GOYAL AskiitiansExpert-IITD
420 Points
13 years ago

Dear nilesh

point 3i will be on y axis and point 4 is on the x axis. length of line joining these points=5

hence z will be somewhere on the line joining these points and between these points.

modz will be distance from origin of point z.

equation of line will be

x/4+ y/3 = 1

3x+4y=12

minimum mod z will be perpendicular distance of this line from origin

apply perpendicular distance formula

3(0)+4(0)-12/√32 + √42

12/5 answer

All the best.

AKASH GOYAL

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