Question

41.41. If the opposite angular points of a
square are (4,3) and (-2,-3), then the side of
the square is
(A) 724 units
(B) 6 units
(C) v12 units
(D) v28 units
Full Marks : 1​

Answer 1

Answer:

the answer is option A)724 units

Answer 2

Let ABCD be a square and let A(3,4) and C(1,-1) be the given angular points. Let B(x,y) be the unknown vertex.

Then, AB=BC

⇒AB2=BC2

⇒(x−3)2+(y−4)2=(x−1)2+(y+1)2

⇒4x+10y−23=0

⇒x=423−10y          ....(i)

In right-angled triangle ABC, we have

AB2+BC2=AC2

⇒(x−3)2+(y−4)2+(x−1)2+(y+1)2=(3−1)2+(4+1)2

⇒x2+y2−4x−3y−1=0     ...(ii)

Substituting the value of x from (i) into (ii), we get

(423−10y)2+y2−(23−10y)−3y−1=0

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