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Chapter 15: Problem 7

The point P lying in the fourth quadrant which is at a distance of 4 units from X-axis and 3 units from Y-axis is (1) \((4,-3)\) (2) \((4,3)\) (3) \((3,-4)\) (4) \((-3,4)\)

Short Answer

Expert verified
Answer: The coordinates of point P are (4, -3).

Step by step solution

01

Finding the X-coordinate

In the fourth quadrant, the X-coordinate of point P is positive. We are given that the distance from the X-axis is 4 units. Therefore, the X-coordinate of point P is 4.
02

Finding the Y-coordinate

In the fourth quadrant, the Y-coordinate of point P is negative. We are given that the distance from the Y-axis is 3 units. Therefore, the Y-coordinate of point P is -3.
03

Writing the coordinates

Combining the X-coordinate and the Y-coordinate, we get the coordinates of point P as \((4, -3)\).
04

Choosing the correct option

Among the given choices, option (1) \((4,-3)\) represents the correct coordinates of the point P lying in the fourth quadrant with the given distances from the X-axis and the Y-axis. So, the answer is (1) \((4,-3)\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Quadrants
In coordinate geometry, the plane is divided into four quadrants by the X-axis and Y-axis. These quadrants help locate the position of a point based on its signs and values. The first quadrant is where both X and Y coordinates are positive. In the second quadrant, the X-coordinate is negative, and the Y-coordinate is positive. Moving to the third quadrant, both coordinates are negative. Finally, the fourth quadrant has a positive X-coordinate and a negative Y-coordinate. Understanding these sign conventions is crucial in identifying a point's position.
Distance from axis
When a point is described by its distance from either the X-axis or the Y-axis, it's important to remember that this distance is always positive. However, the actual coordinates will depend on the quadrant. For instance, if a point is 4 units away from the X-axis, this could mean the Y-coordinate is 4 or -4, depending on the position. Similarly, 3 units from the Y-axis can mean the X-coordinate is 3 or -3. The quadrant plays a key role in determining the signs of these coordinates.
Coordinates of a point
Coordinates are a pair of numbers that define a point's exact position on a plane. They are written as (X, Y) , where X is the horizontal position, and Y is the vertical position. For any coordinate, knowing the positive or negative sign helps identify its placement in a specific quadrant. For example, a point with coordinates (4, -3) is in the fourth quadrant, as the X-coordinate is positive and the Y-coordinate is negative. It's essential to comprehend both the values and signs to accurately pinpoint a location.
X-axis and Y-axis
The X-axis and Y-axis are two perpendicular lines that intersect at the origin (0, 0), dividing the plane into four quadrants. The X-axis runs horizontally and measures the horizontal distance (left or right), while the Y-axis runs vertically, measuring the vertical distance (up or down). These axes serve as reference lines to determine the coordinates of any point on the plane. Along the X-axis, values increase positively to the right and negatively to the left. On the Y-axis, values increase positively upwards and negatively downwards. Understanding these directions is fundamental to mastering coordinate geometry.

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