Question

ABCD is a square whose vertex A lies on
the origin. The coordinates of the
mid-point of the diagonal AC are (p/2,1)
Find the value of p the area of square
ABCD is 20 sq units.​

Answer 1

Given,

Vertex A lies on the origin.

The coordinates of the mid-point of the diagonal AC are (p/2,1)

Area of square ABCD is 20 sq units.

To find,

The value of "p".

Solution,

Coordinate of point A = 0,0

Let, coordinate of point C = (x,y)

Midpoint of AC = (x+0)/2 , (y+0)/2 = (x/2,y/2)

According to the data mentioned in the question,

x/2 = p/2

x = p

And,

y/2 = 1

y = 2

Coordinate of point C = (p,2)

Length of AC = ✓(p-0)²+ (2-0)² = ✓(p²+4) units

Length of one side of the square = ✓(p²+4)/✓2 unit

Area = [✓(p²+4)/✓2]² = (p²+4)/2 units

According to the data mentioned in the question,

(p²+4)/2 = 20

p²+4 = 40

p² = 36

p = ±6

Hence, Value of P will be ±6