Question

Write the coordinates of points A, B, C, D, E and F on the cartesian plane.

Answer 1

To write the x – coordinate of a point, see its distance from the y – axis and to write the y – coordinate of a point, see its distance from the x – axis. Use the information that: - if a point lies in ${{1}^{st}}$ quadrant then both of its coordinates are positive, if the point lies in ${{2}^{nd}}$ quadrant then its x – coordinate is negative and y – coordinate is positive, if the point lies in ${{3}^{rd}}$ quadrant then both x and x and y – coordinates are negative and if a point lies in ${{4}^{th}}$ quadrant then its x – coordinate is positive and y – coordinate is negative. If a point lies on x - axis then its y - coordinate is 0 and if it lies on y – axis then its x – coordinate is 0.

Complete step-by-step answer:
Here, we have been given a graph on which six points A, B, C, D, E and F are plotted and we have been asked to write the coordinates of these points. So, we have,

(i) For point A,
Here, we can see that point lies in ${{2}^{nd}}$ quadrant, so its x – coordinate will be negative and y - coordinate will be positive. Now, the distance of the point from the x axis is 1 unit and from the y – axis is 2 units. Hence, the coordinates of the point A can be written as A (-2, -1).
(ii) For point B,
Here, we can see that the point lies in ${{1}^{st}}$ quadrant, so its x and y – coordinate will both be positive.
Now, the distance of the point from the x – axis is 4 units and from the y – axis is 3 units. Hence, the coordinates of the point B can be written as B (3, 4).
(iii) For point C,
Here, we can see that the point lies in ${{4}^{th}}$ quadrant, so its x – coordinate will be positive and y – coordinate will be negative.
Now, the distance of the point from the x – axis is 3 units and from the y – axis is 1 unit. Hence, the coordinates of the point C can be written as C (1, -3).
(iv) For point D,
Here, we can see that the point lies in ${{3}^{rd}}$ quadrant, so it's both x and y – coordinate will be negative.
Now, the distance of the point from the x – axis is 2 units and from the y – axis is 4 units. Hence, the coordinates of the point D can be written as D (-2, -4).
(v) For point E,
Here, we can see that the point lies on the positive y – axis, therefore its x – coordinate will be 0 and y – coordinate will be positive.
Now, the distance of the point from the x – axis is 3 units. Hence, the coordinates of the point E can be written as E (0, 3).
(vi) For point F,
Here, we can see that the point lies on the positive x – axis, therefore, its y – coordinate will be 0 and x – coordinate will be positive.
Now, the distance of the point from the y – axis is 4 units. Hence, the coordinates of the point F can be written as F (4, 0).

Note: One must remember the signs of coordinates in all the quadrants otherwise you will not be able to solve the question. Remember that the coordinates of a point is negative or positive but its distance from the axes cannot be negative. This is because distance is a scalar quantity and hence it is always positive. You can see that we have not written any of the point’s distances as negative value. You must remember all the rules of writing the coordinates of a point.