Question

Case study based I TREE PLANTATION

The class X students of a school have been allotted a rectangular plot of

land for this gardening activity. Sapling of rose are planted on the boundary

at a 1m from each other. There is a rectangular grazing lawn in the plot as

shown in the figure.

a. Find the co-ordinates of point Q and S are

i)

(2,3), (6,6) ii) (5,3), (1,6) iii) (4,3), (2,6)

iv) (6, 3), (1, 6)

b. Find the distance between Q and S

i)

5 units ii) 4 units iii) 3 units iv) None of those

c. Find the area of the rectangle PQRS

i)

12 sq unit ii) 16 sq unit iii) 9 sq unit

iv) 15 sq unit

d. Find the mid points of PR

i)

(4, ଵ଴

ଶ

) ii) (3,

ଽ

ଶ

) iii) (4,

ଽ

ଶ

) iv) (଻

ଶ

,

ଽ

ଶ

)

e. If the point ‘G’ divides the line QR in the ratio 2:1, then coordinates of G are

i)

(4,5) ii) (6, 5) iii) (5,5) iv) (3,5​

Answer 1

Step-by-step explanation:

) If we take A as origin then AD is X-axis and AB is the Y-axis Then the coordinates of the vertices of △PQR is

P=(4,6),Q=(3,2),R=(6,5)

(ii) If we take C as origin then CB is X-axis and CD is the Y-axis Then the coordinates of the vertices of △PQR is

P=(12,2),Q=(13,6),R=(10,3)

Area of the triangle =

2

1

[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]

First case-

Area of △PQR=

2

1

[4(2−5)+3(5−6)+6(6−2)]

=

2

1

(4×−3+3×−1+6×4)

=

2

1

(−12−3+24)=

2

9

Sq.unit

Second case-

Area of △PQR=

2

1

[12(6−3)+13(3−2)+10(2−6)]

=

2

1

(12×3+13×1+10×−4)

=

2

1

(36+13−40)=

2

9

Sq.unit

Hence we observed that the area of the triangle in both case is equal.