Position of a Point

Summary

This math recipe will help you determine the position of a point, whose coordinates are known, on the XY plane.

Skill Level

Easy

Time

Approx. 30 sec

Ingredients

Coordinates of the point: A(x, y)

Method

To determine the position of A(x, y) on the XY plane, we’ll use the following table.

Condition	Position
x > 0, y > 0	1st quadrant
x < 0, y > 0	2nd quadrant
x < 0, y < 0	3rd quadrant
x > 0, y < 0	4th quadrant
x > 0, y = 0	Positive X-axis
x < 0, y = 0	Negative X-axis
x = 0, y > 0	Positive Y-axis
x = 0, y < 0	Negative Y-axis
x = 0, y = 0	Origin

Examples

Example 1 Indicate the position of the following points on the XY plane.

1. P (5, -3)
2. Q (-6, 2)
3. R (7, 4)
4. S (-1, -4)

Solution For each part, we’ll refer to the table above.

1. Here, x > 0 and y < 0. Therefore, P lies in the 4^th quadrant.
2. Here, x < 0 and y > 0. Therefore, Q lies in the 2^nd quadrant.
3. Here, x > 0 and y > 0. Therefore, R lies in the 1^st quadrant.
4. Here, x < 0 and y < 0. Therefore, S lies in the 3^rd quadrant.

The figure shows the above points on the XY plane.

Example 2 Indicate the position of the following points on the XY plane.

1. A (-3, 0)
2. B (0, 2)
3. C (5, 0)
4. D (0, -4)
5. E (0, 0)

Solution For each part, we’ll refer to the table above.

1. Here, x < 0 and y = 0. Therefore, A lies on the negative X-axis.
2. Here, x = 0 and y > 0. Therefore, B lies on the positive Y-axis.
3. Here, x > 0 and y = 0. Therefore, C lies in the positive X-axis.
4. Here, x = 0 and y < 0. Therefore, D lies in the negative Y-axis.
5. Here, x = 0 and y = 0. Therefore, E lies on the origin.

The figure shows the above points on the XY plane.

That’s it for this recipe. Hope you found it helpful.

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