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Question

The two opposite vertices of a square as shown in the figure are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.


A

B= (0, 1) and D= (1, 4)

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B

B= (1, 4) and D= (1, 0)

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C

B= (4, 1) and D= (0, 1)

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D

B= (1, 0) and D= (1, 4)

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Solution

The correct option is D

B= (1, 0) and D= (1, 4)


O is the point of intersection of AC and BD so O is the midpoint of AC. AC is parallel to X-axis since its y-coordinates are constant.

AC= difference of x coordinates of A and C

=13

= 4

AO = AC2

= 2

Let coordinates of 'O' be (x,2)

{x coordinate of O} - {x coordinate of A} = 2 ( AO = 2)

(x-(-1)) = 2

x=1

O = (1,2)

Diagonals of square are perpendicular to each other so BD will be parallel to Y-axis.

Now AO = BO ( diagonals of a square are equal and bisect each other)
BO = 2

Let B = x1,y1

{y coordinate of O} - {y coordinate of B} = 2

2y1=2

y1=0

and {x-coordinate of B} = {x-coordinate of O}

x1=1

B = (1, 0)
and {y coordinate of D} - {y coordinate of B} = 4 ( BD = 4)

y coordinate of D - 0 = 4

y coordinate of D = 4

D = (1,4)
xcoordinate of D=xcoordinate of B)


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