Question

The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity .sapling of Gulmohor are planted on the boundary at a distance of 1m from each other.there is a rectangular grassy lawn in the plot as shown .the students are to show seeds of flowering plants on the remaining area of the plot

Answer 1

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the class 10th student of a secondary School in krishi Nagar have been allotted a rectangular plot of land for their gardening activities sapling of gulmohar planted on the boundary at a distance of 1 metre from each other there is a rectangular grassy lawn in the figure shown in the figure the students are to sow seeds of flowering plant on remaining area of the plot.

1. taking A as origin find the coordinates of the vertices of triangle.
2. taking C as origin find the coordinates of the vertices of triangle.
3. find the area of triangle in these cases.

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1st condition :- Taking A as origin .

Then the coordinates of A will be (0,0)

°→ Here horizontal line is x axis and vertical is y axis .

°→ Drawing perpendicular from each point i.e P, Q and R to both axis . ( as shown in the attachment )

°→ Coordinates :- P(4,6) , Q (3,2) and R ( 6,5)

2nd condition:- Taking C as origin .

Then coordinate of C will be (0,0)

°→ Draw perpendicular similar to 1st condition .

°→ Coordinates :- P (-12,-2) , Q (-13,-6) and R(-10,-3)

Area of Triangle in both conditions .

A as origin

x1 = 4 x2 = 3 x3 = 6

y1 = 6 y2 = 2 y3 = 5

$area \: = \frac{1}{2} (x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))$

∆ = 1/2 [ 4 (2-5) + 3(5-6) + 6(6-2) ]

∆ = 1/2 [ -12 -5 + 24]

$\triangle \: = \frac{9}{2}$

C as origin :-

x1 = -12 x2 = -13 x3 = -10

y1 = -2 y2 = -6 y3 = -3

∆' = 1/2 [ -12(-6+3) + -13(-3+2) + -10(-2+6) ]

∆' = 1/2 [ 36 + 13 - 40 ]

$\triangle = \frac{9}{2}$

Hence area is same in both conditions