Question

The ends of a diagonal of a square have the co-ordinates (a, 1) and (-1, a). Find
value of a for which the area of square is 50 square units.
[3]
(a) +10
(b) 15
(c) +7
(d) +9​

Answer 1

Step-by-step explanation:

Area of square =Side ^2Side

2

So,Side ^2=40Side

2

=40

Side =\sqrt{40}Side=

40

Side =2\sqrt{10}Side=2

10

Length of diagonal of square = \sqrt{2}a=\sqrt{2}(2\sqrt{10})=2\sqrt{20}

2

a=

2

(2

10

)=2

20

Coordinates of (-2,p) and (p,2)

Formula : d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=

(x

2

−x

1

)

2

+(y

2

−y

1

)

2

d=\sqrt{(p+2)^2+(2-p)^2}d=

(p+2)

2

+(2−p)

2

d=\sqrt{p^2+4+4p+4+p^2-4p}d=

p

2

+4+4p+4+p

2

−4p

d=\sqrt{2p^2+8}d=

2p

2

+8

p=6p=6

Hence the value of p is 6