Question

A school launched a 'go green compaign'in a city.
Each of its student is asked to plant three saplings.
Tanya and Vedika planted trees in a rectangular
land as shown in figure. (V, indicates saplings
planted by Vedika whereas T by Tanya). Both argue
that their saplings are in straight line.
(1) Find out who is correct in judging straightness.
of saplings?
(it) Find the area over which the plantation is
spread.

Answer 1

Answer:

(1) No one is correct in judging straightness.

of saplings.

(2) The area is 48 $unit^2$.

Step-by-step explanation:

(1)

Vedika has planted trees at (-4, 4), (-2, 3) and (8, 2).

A line passing through (-4, 4) and (-2, 3) can be written as $y-4=(\frac{4-3}{-4+2} )(x+4)\\y-4=\frac{-1}{2} (x+4)\\2y-8=-x-4\\2y+x = 4$.

The point (8, 2) does not lies on the above equation, hence Vedika's  saplings are not in straight line.

Tanya has planted at (1,1), (2, 5) and (3, 5).

A line passing through (1, 1) and (2, 5) can be written as $y-1=(\frac{5-1}{2-1} )(x-1) \\y-1=4x-4\\4x-y=3$.

The point (3, 5) does not lies on the above equation, hence Tanya's saplings are not in a straight line.

(2)

The lowest y-ordinate is 1 and the highest y-ordinate is 5.

The lowest x-ordinate is -4 and the highest x-ordinate is 8.

The length of the rectangular area is [8 - (-4)] = 12 and breadth of the rectangular area is (5 - 1) = 4.

The area is $12\times4 = 48 unit^{2}$