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

Answer the following Questions.
i) Find the coordinates of point E Where Esha has plant her flower plant.
a) (5,6)
b) (6,5)
c) (5.5)
d) (6,7)

ii) Find the area of triangle ECD
a) 5.6 unit
b) 6.6 unit
c) 7.6 unit
d) 8.9 unit
iv) The distance between C and D is
a) 5 unit
b) 5.5 unit
c) 6 unit
d) 7 unit
v) Name the type of triangle form with the points ACD.
a) Scalene
b) Isosceles
c) Equilateral
d) None of the above​

Answer 1

Answer:

1) b. 6,5

2) sorry!!!

4) d. 7 units

5) d.none of the above

Step-by-step explanation:

for 2) sorry , Mera answer to 10.5 square units aaraha h

for 5) triangle ACD is a right angled triangle

but , here we can say it sacalene triangle

too . as all three sides of triangle ACD is

vary from each other

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 Esha wanted to plant her flower in this area. The teacher instructed Esha 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 Esha has to plant his flower plant.

a) (5,6)

b) (6,5)

c) (5.5)

d) (6,7)

Ans: Let coordinates of Esha 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).

Option b is correct.

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.

vi) Name the type of triangle form with the points ACD.

a) Scalene

b) Isosceles

c) Equilateral

d) None of the above

Ans: A(3,7),C(3,2), D(10,2)

AC=5 units

DC=7 units

AD=8.6 units

All sides are of different length.So, ∆ACD is a scalene right triangle.

Option a 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.

vi) Option a is correct.

Hope it will help you

*Remark: Mistakes are corrected.

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