Question

If point A(5, P) , B(1, 5) , C(2, 1) and D(6, 2) from a square ABCD then P

Answer 1

S O L U T I O N :

Firstly, attachment a figure of square ABCD a/q:

$\underline{\bf{Given\::}}$

• A(5,P)
• B(1,5)
• C(2,1)
• D(6,2)

$\underline{\bf{Explanation\::}}$

Some properties remind :

• In square all sides are equal & parallel present.
• In square each angle be 90°
• AB = BC = CD = AD

A/q

$\underline{\underline{\tt{Using\:by\:formula\:of\:Distance\::}}}$

$\boxed{\bf{D = \sqrt{(x_2 - x_1 )^{2} + (y_2 - y_1)^{2}}}}$

Take point AB of square, we get;

$\mapsto\tt{AB = \sqrt{(1-5)^{2} + (5-P)^{2}}}$

$\mapsto\tt{AB = \sqrt{(-4)^{2} + (5-P)^{2}}}$

$\mapsto\tt{AB = -4 + 5-P}$

$\mapsto\tt{AB = 1-P}$

Take point DC of square, we get;

$\mapsto\tt{DC = \sqrt{(2-6)^{2} + (1-2)^{2}}}$

$\mapsto\tt{DC = \sqrt{(-4)^{2} + (-1)^{2}}}$

$\mapsto\tt{DC = -4 + (-1)}$

$\mapsto\tt{DC = -4 -1}$

$\mapsto\tt{DC = -5}$

Now,

As we know that AB || DC according to the property of square.

So, AB = DC

$\mapsto\tt{AB = DC}$

$\mapsto\tt{1-P = -5}$

$\mapsto\tt{-P = -5-1}$

$\mapsto\tt{\cancel{-}P = \cancel{-}6}$

$\mapsto\bf{P = 6}$

Thus,

The value of P will be 6 .

Answer 2

Answer:

a) 7

b) 3

c) 6

d) 8

For this question the answer is 6