Question

The coordinates of a square are: (7,2), (7,7), (2,7) and (?,?)

Answer 1

(7,7) - (2,7) the change along x-axis is 5 units

(7,7) - (7,2) the change along y-axis is 5 units

The missing point (2,x) = (2, 7 - 5) = (2,2)

The coordinates of the square are hence (7,2), (7,7), (2,7) and (2,2)

Answer 2

(2,2)

Explanation:

Let's assume the four vertices of square be A(7,2), B(7,7), C(2,7) and D(x,y).

Now coordinates of vertices D needs to be found. For that use the following property of a square:

• Diagonal of square bisect each other.

Refer to figure 1 to for understanding below calculations.

Since diagonal AC and BD bisect each other at point O(p,q). Therefore O is the mid-point of both AC and BD.

Now since O is mid-point of AC. Therefore,

`O(p,q)=\left ((7+2)/(2),(2+7)/(2)\right )=\left ( (9)/(2),(9)/(2)\right )`

Also since O is mid-point of BD. Therefore,

`O(p,q)=\left ((7+x)/(2),(7+y)/(2)\right )`

`\Rightarrow \left ( (9)/(2),(9)/(2)\right )=\left ((7+x)/(2),(7+y)/(2)\right )`

`\Rightarrow(7+x)/(2)=(9)/(2)\Rightarrow x=2`

Similarly,

`(7+y)/(2)=(9)/(2)\Rightarrow y=2`

Thus coordinates of D are (2,2)