Question

Signs of abscissa and ordinate of a point in the \[III\]Quadrant respectively are
A. \[ + , + \]
B. \[ - , - \]
C. \[ - , + \]
D. \[ + , - \]

Answer 1

Hint: We use the knowledge of abscissa and ordinate of a point and determine their signs using the Quadrant diagram.
* A quadrant diagram is a diagram of a Cartesian plane that is divided into four quadrants on the basis of signs of x-coordinate and y-coordinate of the point.

* The Abscissa of a point is the perpendicular distance of a point from the y-axis. The value of x-coordinate is called abscissa
* Ordinate of a point is the perpendicular distance of a point from x-axis. The value of y-coordinate is called ordinate.

Complete step-by-step answer:
We have to find the signs of abscissa and ordinate of a point in the \[III\]Quadrant.
Since the quadrant diagram tells us the location of each quadrant, the third quadrant is the quadrant that lies on the bottom left of the diagram.
Let A be a point on the Cartesian plane.
Then point A has coordinates \[(x,y)\](say)
From the definition of abscissa we can say the value of abscissa is ‘x’.
From the definition of ordinate we can say the value of ordinate is ‘y’.
Let us take the point in the third quadrant. Draw a diagram of a point in the third quadrant.

Since the perpendicular distance of point A from the x-axis is negative\[ \Rightarrow \]Abscissa is negative.
Since the perpendicular distance of point A from the y-axis is negative\[ \Rightarrow \]Ordinate is negative.
\[\therefore \]Sign of abscissa and ordinate in the third quadrant is \[ - , - \]

Option B is the correct answer.

Note: Students can make minor mistakes in choosing the option if they don’t remember the sequence in which quadrants are written, keep in mind we always move in anticlockwise direction and we start from the quadrant that has both abscissa and ordinate as positive.