Question

Write the coordinates of the vertices of a rectangle whose length and breadth are 5 units and 3 units, respectively. One vertex at the origin, the longer side lies on the x-axis and one of the vertices lie in the third quadrant.
(A). (0,0), (5,0), (0,-3) & (5,-3)
(B). (0,0), (0,-5), (3,0) & (3,-5)
(C). (0,0), (-5,0), (0,-3) & (-5,-3)
(D). (0,0), (5,0), (0,3) & (5,3)

Answer 1

Hint: Use the property of the rectangle that opposite sides are equal and the angle between adjacent sides is equal to $90{}^{\circ }$ . Also, you need to ensure that one of the vertices of the rectangle lies in the third quadrant, as asked in the question.

Complete step-by-step solution -
Now according to the question, one of the vertices is the origin, i.e., one of the vertices of the rectangle has coordinates (0,0). Now let us draw a diagram to check all the possible cases of rectangles which have one of their vertices to be the origin and the longer side of the rectangle lying along the x-axis.

Now among the four rectangles, the rectangle ADGI is the one for which one of the vertices lies in the third quadrant.
So, the vertices of the asked rectangle can be found as:
We know D(0,0) and A is at a distance of 5 units from the origin and lies on the negative x-axis. Therefore, we can say that A=(-5,0). Similarly, G is at a distance of 3 units from the origin and lies on the negative y-axis. So, G=(0,-3). And if we compare A and I, they will have their x- coordinate the same, which is -5 and also, G and I have the y-coordinate same, which is equal to -3. Therefore, we can say that I=(-5,-3).
Hence, the answer to the above question is option (c).

Note: You could have also answered the above question by easily eliminating the options, as the only option with one vertex in the third quadrant is option (c), but knowing the method is also important.