# If Points a (5, P) B (1, 5), C (2, 1) and D (6, 2) Form a Square Abcd, Then P = - Mathematics

MCQ

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

• 7

• 3

• 6

• 8

#### Solution

The distance d between two points (x_1 ,y_1)  and  (x_2 , y_2)   is given by the formula

 d= sqrt( (x_1 -x_2)^2 + (y_1 - y_2)^2)

In a square all the sides are equal to each other.

Here the four points are A(5,p)B(1,5), C(2,1) and D(6,2).

The vertex ‘A’ should be equidistant from ‘B’ as well as D’

Let us now find out the distances ‘AB’ and ‘AD’.

AB = sqrt((5-1)^2 + (P -5)^2)

AB = sqrt((4)^2 + (p -5)^2)

AD = sqrt((5-6)^2 + (p-2)^2)

AD = sqrt((-1)^2 + (p-2)^2)

These two need to be equal.

Equating the above two equations we have,

sqrt((4)^2 +(p -5)^2 ) = sqrt((-1)^2 + (p-2)^2)

Squaring on both sides we have,

(4)^2 +(p -5)^2 = (-1)^2 + (p - 2)^2

16+p^2 + 25 - 10 p = 1 + p^2 + 4 - 4p

6p = 36

p = 6

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 6 Co-Ordinate Geometry
Q 31 | Page 65