Question

(0,-1) and (0,3) are the two vertices of a square. The other two vertices are​

Answer 1

Answer:

Let the points be B(x1,y1) and D(x2,y2) point of

BD=(x1+X22,y1+y22) and mid point of AC=(0,1)

We know, mid point of both the diagonal lie on the same point E.

⇒x1x22=0 and y1+y22=1

⇒x1+x2=0 ....(i)

and y1+y2=2 .......(ii)

Slope of BD× slope of AC=−1

(y1−y2)(x1−x2)×(3+1)(0−0)=−1

⇒y1−y2=0 ....(iii)

Solving Eqs. (ii) and (iii), we get

y1=1,y2=1

Now, slope of AB× slope of BC=−1

⇒(y1+1)(x1−0)×(y1−3)(x1−0)=−1

⇒(y1+1)(y1−3)=−x21

⇒2(−2)=−x21  [∵y1=1]  

⇒x1=±2

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