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A diagonal of rhombus A B C D is member ...

A diagonal of rhombus `A B C D` is member of both the families of lines `(x+y-1)+lambda(2x+3y-2)=0` and `(x-y+2)+ lamda(2x-3y+5)=0` and rhombus is (3, 2). If the area of the rhombus is `12sqrt(5)` sq. units, then find the remaining vertices of the rhombus.

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To solve the problem step by step, we will follow the process outlined in the video transcript while providing clear explanations for each step. ### Step 1: Understanding the Problem We have a rhombus \(ABCD\) with one vertex \(B(3, 2)\) and the area given as \(12\sqrt{5}\) square units. We also know that one diagonal is a member of two families of lines. ### Step 2: Finding the Intersection of the Families of Lines The equations of the lines from the two families are: 1. \(x + y - 1 + \lambda(2x + 3y - 2) = 0\) ...
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