Question

16. If points A(5, p), B(1,5), C( 2, 1) and D(6, 2) form a square ABCD, then p=

I want with solution..
plse fast ​

Answer 1

Answer:

Vertices of a square are A(5, p), B(1, 5), C(2, 1) and D(6, 2).

The diagonals bisect each other at O

O is the mid-point of AC and BD

O is mid-point of BD, then

CO-ordinates of O will be \(\left(\frac{1+6}{2}, \frac{5+2}{2}\right)\)

or \(\left(\frac{7}{2}, \frac{7}{2}\right)\)

\(\because \) O is mid-point of AC also

\(\therefore \frac{p+1}{2}=\frac{7}{2} \Rightarrow p+1=7\)

\(\Rightarrow\) p = 7 - 1 = 6

Therefore the choice is: C