Question

On day, Mohan visited his friend's apartment. From his balcony, he observed that there is

flower bed on the ground which is in the shape of a parallelogram. Four red colour poles are

there at the corners of the garden. He draws the sketch of the flower bed on a graph paper as

shown in below figure.

(a) The coordinates of the vertex D are

(i) (3, 4) (ii) (4, 3) (iii) (3, 3) (iv) (4, 4)

(b) The coordinates of the point of intersection of the diagonals are:

(i) (5, 5) (ii) (5/2, 5/2) (iii) (5, 5/2) (iv) (5/2, 5)


(c) The length of the side AB is:

(i) 7 units (ii) 6 units (iii) 5 units (iv) none of these


(d) The length of the side AD is

(i) √13 units (ii) 13 units (iii) 14 units (iv) √14 units


(e) If we take A as the origin and AB as x-axis then the cooridnates of M are

(i) (4, 3/2) (ii) (3/2, 4) (iii) (4,4) (iv) (3/2, 3/2



​

Answer 1

(I) (I) 3,4

(II) (III) 5,5/2

Answer 2

Answer:

Concept:

A simple (non-self-intersecting) quadrilateral with two sets of parallel sides is known as a parallelogram in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. The Euclidean parallel postulate or one of its equivalent formulations must be used in order to demonstrate the congruence of opposed sides and opposite angles because both conditions are a direct result of this postulate.

Step-by-step explanation:

Given:

Flower bed on the ground which is in the shape of a parallelogram

Four red color poles are there at the corners of the garden as shown in the given graph.

Find:

The coordinates of the vertex D are

The coordinates of the point of intersection of the diagonals are

The length of the side AB is

The length of the side AD is

If we take A as the origin and AB as the  x-axis then the coordinates of M are
Solution:

(a)  The coordinates of the vertex D are (3, 4)

      That is option (i)

(b) The coordinates of the point of intersection of the diagonals are  

      (5, 5/2) That is option (iii)

(c)   The length of the side AB is 6 units. That is option (ii)

(d)   The length of the side AD is

         $A D^{2}=(2)^{2}+(3)^{2}$

                  = 4 + 9

                  = 13

        $A D=\sqrt{13}$ units  

That is option (i)

(e) If we take A as the origin and AB as the x-axis then the coordinates of    M  are  (4, 3/2)

   That is option (i)

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