Question

9


On the basis of the above information, answer any four of the following questions:
(i) What is the position of the pole c?
(a) (4,5)
(b) (5, 4)
(c) (6,5)
(d) (5,6)
(ii) What is the distance of the pole B from the corner 0 of the park ?
(a) 6/2 units
(b) 3/2 units
(c) 6v3 units
(d) 3/3 units
(iii) Find the position of the fourth pole D so that four points A, B C and D form a parallelogram
(a) (5,2)
(b) (1,5)
(c) (1,4)
(d) (2,5)
(iv) What is the distance between poles A and C ?
(a) 62 units
(b) 3/2 units
(c) 673 units
(d) 3/3 units
(v) What is the distance between poles B and D?
(a) 2/3 units
(b) 28 units
(c) 6/3 units
(d) 26 units​

Answer 1

Answer:

1-(b),2-(a),3-(c),4-(a),5,(d

Step-by-step explanation:

1=(5,4)

2=6√2

3=(1,4)

4=6√2

5=√26

Answer 2

The coordinates of point C are (b) (5 ,4).

The distance of point B from the origin is (a) 6$\sqrt{2}$ units.

The coordinates of point D will be (b) (1 ,5).

The distance between point A and C is (b) 3$\sqrt{2}$ units.

The distance between points B and D is (d) $\sqrt{26}$ units.

Explanation 1

The abscissa of point C in the given figure is 5 and the ordinate is 4. Hence, the coordinates of the point C are (5 ,4).

Explanation 2

We have the coordinates of point B say $(x_{1} ,y_{1} )$ as $(6 ,6)$ and the corner O of the park is the origin say $(x_{2} ,y_{2} )$ which has coordinates (0, 0). Therefore, using distance formula

$D=\sqrt{(x_{2}- x_{1} )^{2}+(y_{2}- y_{1} )^{2} }$

$D=\sqrt{(0-6)^{2}+ (0-6)^{2} }$

$D=\sqrt{36+36}$

$D=6\sqrt{2} units$

Hence, Distance of point B from the origin is $(a)$ $6\sqrt{2}$ units.

Explanation 3

We have, coordinates of point B $(6,6)$ and that of point C $(5,4)$.

We know, in a parallelogram, opposite sides are parallel hence if ABCD is to be a parallelogram then, the slope of BC should be equal to slope of AD since parallel lines have slopes equal.

Hence, slope of BC  will be

$m_{1} =\frac{y_{2} -y_{1} }{x_{2} -x_{1} }$

Substituting the given values, we get

$m_{1}=\frac{4-6}{5-6}$

$m_{1}=\frac{-2}{-1}=2$

Now, from the given options, who along with coordinates of A $(2,7)$ give slope 2 are

1. $(5,2)$    $m_{2}=\frac{2-7}{5-2}=\frac{-5}{3} ;(N.P.)$
2. $(1,5)$    $m_{2}=\frac{5-7}{1-2} =\frac{-2}{-1} =2$

         We get $m_{1} =m_{2}$

Hence, the coordinate of point D will be option $(b)$ $(1,5)$ .

Explanation 4

We have point A $(2,7)$ and point C as $(5,4)$. Substituting the values in distance formula, we get

$D=\sqrt{(5-2)^{2}+(4-7)^{2} }$

$D=\sqrt{9+9} =\sqrt{18}$

$D=3\sqrt{2} units$

Hence, the distance between point A and C is $3\sqrt{2}$ units.

Explanation 5

We have coordinates of point B as $(6,6)$ and that of D as $(1,5)$

Substituting in distance formula, we get,

$D=\sqrt{(1-6)^{2}+ (5-6)^{2} }$

$D=\sqrt{25+1}$

$D=\sqrt{26}$

Hence, the distance between point B and D is $\sqrt{26}$ units.