Question

A long horizontal piece of wood EF is suspended above the ground, as shown in the
diagram, by two ropes EB and F D which are tied to two bamboo poles AB and CD of
equal lengths. The bamboo poles are at equal distances from the edge of wooden piece.
The bamboo poles are supported by two different ropes GB and HD respectively as
shown in the figure.

Answer 1

Answer:

If A is treated as origin then the coordinate of point E will be (1, 3)

If A is treated as origin then the coordinate of point F will be (4, 3)

The slope of thread DH is -3

Step-by-step explanation:

Correct options are:

If A is treated as origin then the coordinate of point E will be (1, 3)

If A is treated as origin then the coordinate of point F will be (4, 3)

The slope of thread DH is -3

Answer 2

Question:

You can find the complete question below in the figure.

Answer:

• The length of wood EF (b) = 3 ft.

• If A is treated as origin then the coordinate of the point "E" will be E(1, 3).

• If A is treated as origin then the coordinate of the point "F" will be   F(4, 3).

• The slope of DH is -3.

Step-by-step explanation:

Given,

Length of wood EF = b ft

Distance between the bamboos AB and CD is AC = 5 ft

Length of the bamboos AB = CD = 4 ft

∠EBA = ∠FDC = 45°

Distance between the either of the edge of the wood and the bamboo is a ft.

Let us consider a straight line drawn from "F" to the bamboo stick perpendicularly and cuts at "X" on the bamboo.

Now we use tangent ratio to find the length "a".

From figure:

$\tan(45) = \frac{FX}{DX}$

⇒ $1=\frac{FX}{DC-XC}$

⇒ $1 = \frac{a}{4-3}$

⇒ a ft = 1 ft.

Therefore, the length of the wood EF = AC - (2×a)

                                                    ⇒  EF = 5 ft - (2×1)

                                                   ⇒  EF (b ft)= 3 ft.

Now if A is treated as origin then the coordinate of the point "E" will be

E(a, 3) i.e. E(1, 3)

And, similarly the point "F" will be F(5-a, 3) i.e. F(4, 3).

Now we can find point H as H(5+a, 1) i.e. H(6,1)

Similarly the point D id D(5, 4)

As we know that two point form of slope is $m = \frac{y_2-y_1}{x_2-x_1}$

here $y_2 = 1,y_1 = 4, x_2 = 6, x_1 = 5$

therefore the slope of DH will be   $\frac{1-4}{6-5}$

⇒ the slope of DH is -3.

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