1 of 3

COORDINATE GEOMETRY

  • Sum based on Distance formula

2 of 3

P

Q

R

S

∴

Diagonal PR

=

(–1

–

3)

2

+

(4

2

–

0)

d1

=

(–4)

2

+

(4)

2

d1

=

16

+

16

∴

∴

d1

=

32

∴

d1

=

2

∴

4

∴

Diagonal QS

=

(–2

–

4)

2

+

(–1

2

–

5)

d2

=

(–6)

2

+

(–6)

2

∴

d2

=

36

+

36

∴

d2

=

72

∴

d2

=

∴

6 2

 

Let the coordinates of P be (x1, y1)

Let the coordinates of R be (x2, y2)

Sol.

P

=

(3,

0),

Q

=

(4,

5),

x1 = 3,

y1 = 0

x2 = –1,

y2 = 4

Which is the formula to find length of PR?

+

–

–

(

)

(

)

x2

x1

y2

y1

2

2

R

=

(–1,

4),

S

=

(–2,

–1)

Let the coordinates of Q be (x1, y1)

Let the coordinates of S be (x2, y2)

Which is the formula to find length of QS?

+

–

–

(

)

(

)

x2

x1

y2

y1

2

2

x1 = 4,

y1 = 5

x2 = –2,

y2 = –1

3 of 3

P

Q

R

S

 

Sol.

P

=

(3,

0),

Q

=

(4,

5),

R

=

(–1,

4),

S

=

(–2,

–1)

∴

Area of rhombus ABCD

=

1

2

×

d1

×

d2

=

1

2

×

2

4

×

2

6

=

2

×

2

×

6

= 24

d1

=

2

4

d2

=

6 2

2

∴

Area of rhombus PQRS is 24 sq. units