Question

Write the coordinates of the vertices of a rectangle whose length and

breadth are 5 and 3 units respectively, one vertex is at the origin, the longer

side lies on the x-axis, and one of the vertices lies in the third quadrant.​

Answer 1

Answer:

Correct option is

C

(0,0),(−5,0),(0,−3) & (−5,−3)

Let the rectangle be OABC with the vertex O at the origin.

Let OA be the longer side.

∴ The co-ordinate of O is O(0,0).

Since one of the vertex is in the third quadrant and the longer side of length 5 units lie on the x-axis, the co-ordinate of A is A(−5,0).

Also, the rectangle lie in the III quadrant.

∴ The side OC will lie on the y-axis to the negative direction.

Then, the length of OC is 3 units.

∴ The co-ordinates of C will be C(0,−3).

Then obviously, the co-ordinates of B will be (−5,−3).

Here, OC∥AB and ∠AOC=90

o

, hence is a rectangle.

Therefore, the vertices of the rectangle are O(0,0),A(−5,0),B(−5,−3),C(0,−3).

Hence, option C is correct.

solution