Question

Find the quadrant or axis on/in which the following point lies.
$\left( {8, - 7} \right)$
A. I
B. II
C. IV
D. None of these

Answer 1

Hint: Any point on the Cartesian system is denoted as (x, y) where x is the x coordinate and y is the y coordinate and the coordinate axes divide the plane into four quadrants into the first quadrant, second quadrant, third quadrant, fourth quadrant. Here we need to check the sign before the point i.e. whether it is positive or negative. As per this we will decide the quadrant.

Complete step-by-step answer:
In the First - Quadrant, both x-coordinate and y-coordinate are positive, i.e., the points on the first - quadrant are (x, y).
In the Second - Quadrant x-coordinate is negative and the y-coordinate is positive, i.e., the points on the second - quadrant are (-x, y).
In the third Quadrant, both x-coordinate and y-coordinate are negative, i.e., the points on the third quadrant are (-x, -y).
In the Fourth -Quadrant x-coordinate is positive while the y-coordinate is negativities, the points on the fourth quadrant are (x, -y).
Any point lying on the x-axis has coordinates of the form $\left( {x,0} \right)$
Any point lying on the y-axis has coordinates of the form $\left( {0,y} \right)$
Here the given point is $\left( {8, - 7} \right)$and we need to find whether the point lies in the I, II, III, IV quadrant.
The x-coordinate of the given point is $8$ and y-coordinate is $ - 7$
Here we can able to note that the x-coordinate in the given point is greater than zero and the y-coordinate is less than zero. That is, the x-coordinate is positive whereas the y-coordinate is negative.
Hence the point $\left( {8, - 7} \right)$ lies in the fourth quadrant because the x-coordinate is positive and the y-coordinate is negative.

Therefore $\left( {8, - 7} \right)$lies in the IV quadrant and option C is the correct answer.

So, the correct answer is “Option C”.

Note: If we are given the point $\left( {8,7} \right)$ to find the quadrant, we can able to say that it will lie in the first quadrant because both the coordinates are positive.
If the given point is of the form $\left( {x,0} \right)$ , then the point will lie on the x-axis for all $x \in \mathbb{R}$
Similarly, if the given point is of the form $\left( {0,y} \right)$ , then the point will lie on the y-axis for all $x \in \mathbb{R}$