Advertisement Remove all ads

# 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 =

#### Options

• 7

• 3

• 6

• 8

Advertisement Remove all ads

#### 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,

AB  =  AD

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?
Advertisement Remove all ads

#### APPEARS IN

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

#### Video TutorialsVIEW ALL 

Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?