Question

In the school garden Ajay(A), Brijesh(B), Chinki(C) and Deepak(D) planted their flower plants of Rose, Sunflower, Champa and Jasmine respectively as shown in the following figure: A fifth student Eshan wanted to plant her flower in this area. The teacher instructed Eshan to plant his flower plant at a point E such that CE: EB = 3:2. 10 7 A13,7) B(8.7) 5 2 D[ 10 2​

Answer 1

Answer:

hey please answer me this question please I also need this

Answer 2

Step-by-step explanation:

Given: In the school garden Ajay(A), Brijesh(B), Chinki(C) and Deepak(D) planted their flower plants [4] of Rose, Sunflower, Champa and Jasmine respectively as shown in the following figure.

A fifth student Eshan wanted to plant her flower in this area. The teacher instructed Eshan to plant his flower plant at a point E such that CE: EB = 3 : 2.

To find: Answer the following questions:

i. Find the coordinates of point E where Eshan has to plant his flower plant.

Ans: Let coordinates of Eshan plant is E(x,y)

Given that: CE: EB = 3 : 2

3 2

C(3,2)•___________•E(x,y)_________•B(8,7)

Section formula: If point P(x,y) divides the line segment AB in m:n,when coordinates of A(x1,y1) and B(x2,y2)

then

$\boxed{\bf x = \frac{mx_2 + nx_1}{m + n} } \\ \\ \boxed{\bf y = \frac{my_2 + ny_1}{m + n}}$

So,

According to section formula

$x = \frac{3 \times 8 + 2 \times 3}{3 + 2}$

$x = \frac{24 + 6}{5}$

$x = \frac{30}{5}$

$\bf x = 6$

and

$y = \frac{3 \times 7 + 2 \times2 }{3 + 2}$

$y = \frac{21 + 4 }{5}$

$y = \frac{25}{5}$

$\bf y = 5$

Coordinates of E(6,5).

ii) Find the area of △ ECD.

a. 9.5 square unit

b. 11.5 square unit

c. 10.5 square unit

d. 12.5 square unit

Ans:

If A(x1,y1), B(x2,y2) and C(x3,y3)

$\boxed{\bf Ar(∆ABC) = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| }$

Here,

Vertices of triangle are E(6,5),C(3,2) and D(10,2)

$Ar(∆ECD) = \frac{1}{2} |6(2 - 2) + 3(2 - 5) + 10(5 - 2)|$

$Ar(∆ECD) = \frac{1}{2} |0 - 9 +30|$

$Ar(∆ECD) = \frac{1}{2} |21|$

Ar(∆EDC)=10.5 sq-unit

Option C is correct.

iii. Find the distance between the plants of Ajay and Deepak.

a. 8.60 unit

b. 6.60 unit

c. 5.60 unit

d. 7.60 unit

Ans:

Distance formula: If P(x1,y1) and Q(x2,y2), then

$\boxed{\bf PQ = \sqrt{ {(x_2 - x_1)}^{2} + ( {y_2 - y_1)}^{2} }}$

To find distance between Ajay and Deepak apply distance formula.

Coordinates of A(3,7) and D(10,2)

$AD = \sqrt{ {(10 - 3)}^{2} + ( {2 - 7)}^{2} }$

$AD = \sqrt{ 49 + 25}$

$AD = \sqrt{74}$

$\bf AD = 8.6 \:$

Option a is correct.

iv. The distance between A and B is:

a. 5.5 units

b. 7 units

c. 6 units

d. 5 units

Ans: A and B lies on the straight line,

thus,

Distance between A(3,7) and B(8,7) is difference of 8 and 3.

AB= 5 units

Option d is correct.

v. The distance between C and D is:

a. 5.5 units

b. 7 units

c. 6 units

d. 5 unit

Ans: C and D lies on the straight line,

thus,

Distance between C(3,2) and D(10,2) is difference of 10 and 3.

CD= 7 units

Option b is correct.

Note*: Distance AB and CD can be calculated by distance formula also.

Final answer:

I) Coordinates of E(6,5)

ii) Option c is correct.

iii) Option a is correct.

iv) Option d is correct.

v) Option b is correct.

Hope it will help you.

Remark*: Question are added for this.

Learn more:

1) Find the area of the given regular octagon having each side equal to 5 cm. HC =11 cm and AL = 4 cm. B. 4 cm С H L 11 ...

https://brainly.in/question/48604843

2) The area of the largest possible square inscribed in a circle of radius 2 cm is: a) 8 cm? c) 412 cm? 2 2. 2 b) 4 cm ...

https://brainly.in/question/48193648