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Question

0,-1 and 0,3 are two opposite vertices of a square. The other two vertices are


A

0,1,0,-3

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B

3,-1,0,0

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C

2,1,-2,1

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D

2,2,1,1

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Solution

The correct option is C

2,1,-2,1


Explanation for the correct option:

Step 1. Draw a square ABCD with the diagonals AC and BD which are intersecting at E

Let A(0,1) and C(0,3) be its two opposite vertices.

Step 2: Find the diagonal AC and length of each side

Length of diagonal AC=(00)2+(3+1)2=16=4

Length of each side =diagonal2

=42=22

Now, Let the co-ordinates of another vertex of the square B be (x1,y1)

Step 3: Find the y coordinate

The distance of vertex Bfrom vertex Aand vertex Cwill be equal.

(x10)2+(y1+1)2=(x10)2+(y13)2

x12+y12+2y1+1=x12+y126y1+9

8y1=8

y1=1

Step 4: Find the x coordinate

Distance BA=22

(x10)2+(y1+1)2=22

x12+y12+2y1+1=8

x12+4=8 [y1=1]

x12=4

x1=±2

Therefore, The required two vertices of the square ABCD are (+2,1) and (2,1).

Hence, option ‘C’ is Correct.


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