17) A rectangle has two opposite vertices at the points (1,2) and (5,5) . If the other vertices lies on the line x=3, find the equations of the sides of the rectangle.

Dear Student,

Please find below the solution to the asked query :


So, other 2 vertices are B3,1 and D3,6.Now, equation of line joining x1,y1 and x2,y2 isy-y1x-x1 = y2-y1x2-x1So, equation of AB joining A1,2 and B3,1 isy-2x-1 = 1-23-1x+y = 3equation of BC joining B3,1 and C5,5 isy-1x-3 = 422x-y = 5equation of CD joining C5,5 and D3,6 is    y-6x-3 = -12x+2y= 15equation of DA joining D3,6 and A1,2 is    y-2x-1 = 422x-y = 2

Hope this would clear your doubt.

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