If (4,1) and (4,7) are the coordinates of a diagonal of a square. Whic

Question

If (4,1) and (4,7) are the coordinates of a diagonal of a square. Which could be coordinates of a vertex of the square?​

A. (0.5, 4)​

B. (0.5, 5)​

C. (1, 4)​

D. (1, 5)​

E. (1.5, 4)​

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ElninoEffect · Answer

If (4,1) and (4,7) are the coordinates for the diagonal of a square then from the properties of the square we know that:
a= d/root2 | where a is side of the square and d is diagonal.

Let's find the d which is the distance between (4,1) and (4,7) = Root  = 6 units.

So a will be = 6/root2 = 3*root2

Now checking all options for the same distance from any of the two given vertex (4,1) and (4,7) we will find that only option C will fetch us the same value.

Hence C is the answer.

DashingNightmare2 · Answer

Here we need t take care of 2 conditions
1. Coordinates of diagonal are same as coordinates of 2 sides, For any vertex distance from these 2 given points must be same
2. Since each angle of square is 90, it will follow right angled triangle property 
 AB^2+ BC^2 =AC^2 
Where AB and BC are distance of new point from the 2 vertices and AC is diagonal

A,C,E satisfy condition 1.
Among them, only C satisfies condition 2

Hence, IMO  C

bv8562 · Answer

Properties of  DIAGONALS  in a  SQUARE :

1. Diagonals are of equal length.
2. Diagonals bisect each other.
3. Diagonals intersect each other at 90 degree.

Given, the coordinates of a diagonal of a square = (4,1) and (4,7)

Since, diagonals in a SQUARE bisect each other, therefore the other diagonal must pass through the MID-POINT of the given diagonal.

Mid-point  = (X1+X2)/2, (Y1+Y2)/2 = (4+4)/2, (1+7)/2 = (4,4)

From, above we know that the other diagonal must pass through point (0,4)

Length of the given diagonal = √(X1-X2)^2 + (Y1-Y2)^2 = √(4-4)^2 + (7-1)^2 = 6 units
∴ Length of the other diagonal should also be = 6 units

Since, both the diagonals must bisect each other, therefore, only  option (C)  satisfies this condition.

bumpbot · Answer

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If (4,1) and (4,7) are the coordinates of a diagonal of a square. Whic

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If (4,1) and (4,7) are the coordinates of a diagonal of a square. Whic

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