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

Answer:

(2,2)

Step-by-step 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,

$O(p,q)=\left (\frac{7+2}{2},\frac{2+7}{2}\right )=\left ( \frac{9}{2},\frac{9}{2}\right )$

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

$O(p,q)=\left (\frac{7+x}{2},\frac{7+y}{2}\right )$

$\Rightarrow \left ( \frac{9}{2},\frac{9}{2}\right )=\left (\frac{7+x}{2},\frac{7+y}{2}\right )$

$\Rightarrow\frac{7+x}{2}=\frac{9}{2}\Rightarrow x=2$

Similarly,

$\frac{7+y}{2}=\frac{9}{2}\Rightarrow y=2$

Thus coordinates of D are (2,2)