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A rectangle has two opposite vertices at...

A rectangle has two opposite vertices at the points `(1,2)a n d(5,5)dot` If the other vertices lie on the line `x=3` , find the equations of the sides of the rectangle.

Text Solution

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Let A,B,C,D be the four vertices The, A=`(1,2)` and C=`(5,5).`
Since the other two vertices B and D lie on the line x=3, therefore, let `B=(3,y_1​) and D=(3,y_2​).`
Since AC and BD bisect ,they have same middle point
⇒`(y_1​+y_2)/2​​=(2+5)/2​⇒y_1​+y_2​=7 ...(1)`
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Knowledge Check

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