Understanding Point Coordinates

Oct 13, 2025 by magicalceylontours.com 102 views

Introduction

When working with points in a coordinate plane, it's essential to understand the relationships between them. In this article, we will explore the properties of points and determine which sentence about the given points is true.

Understanding Point Coordinates

To begin, let's recall that each point in a coordinate plane has a unique set of coordinates, represented as (x, y). The x-coordinate represents the point's horizontal position, while the y-coordinate represents its vertical position.

Given Points

We are given four points: A, B, C, and D, with coordinates (-8, 1), (-2, 4), (-3, -1), and (-6, 5), respectively.

Analyzing the Points

To determine the relationship between these points, we need to examine their coordinates. Let's start by comparing the x-coordinates of each point.

Horizontal Comparison

Point A has an x-coordinate of -8.
Point B has an x-coordinate of -2.
Point C has an x-coordinate of -3.
Point D has an x-coordinate of -6.

From this comparison, we can see that point D has the most negative x-coordinate, while point B has the least negative x-coordinate.

Vertical Comparison

Point A has a y-coordinate of 1.
Point B has a y-coordinate of 4.
Point C has a y-coordinate of -1.
Point D has a y-coordinate of 5.

Here, we can observe that point C has the most negative y-coordinate, while point B has the highest y-coordinate.

Determining the Relationship

Now that we have analyzed the coordinates of each point, let's examine the given sentences to determine which one is true.

Sentence A

Sentence A states that point A is the point with the most negative x-coordinate.

Sentence B

Sentence B states that point B is the point with the least negative x-coordinate.

Sentence C

Sentence C states that point C is the point with the most negative y-coordinate.

Sentence D

Sentence D states that point D is the point with the highest y-coordinate.

Conclusion

After analyzing the coordinates of each point, we can conclude that:

Point D has the most negative x-coordinate, making Sentence A false.
Point B has the least negative x-coordinate, making Sentence B true.
Point C has the most negative y-coordinate, making Sentence C true.
Point D has the highest y-coordinate, making Sentence D false.

Therefore, the true sentences about the points are:

Sentence B: Point B is the point with the least negative x-coordinate.
Sentence C: Point C is the point with the most negative y-coordinate.

The final answer is B and C.

Introduction

In our previous article, we explored the properties of points in a coordinate plane and determined which sentence about the given points was true. In this article, we will answer some frequently asked questions about points in a coordinate plane.

Q: What is the difference between the x-coordinate and the y-coordinate?

A: The x-coordinate represents the point's horizontal position, while the y-coordinate represents its vertical position.

Q: How do I determine the relationship between two points in a coordinate plane?

A: To determine the relationship between two points, you can compare their x-coordinates and y-coordinates. You can also use the distance formula to calculate the distance between the two points.

Q: What is the distance formula?

A: The distance formula is a mathematical formula used to calculate the distance between two points in a coordinate plane. The formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where d is the distance between the two points, and (x1, y1) and (x2, y2) are the coordinates of the two points.

Q: How do I determine if two points are collinear?

A: Two points are collinear if they lie on the same line. To determine if two points are collinear, you can calculate the slope of the line passing through the two points. If the slope is the same for both points, then they are collinear.

Q: What is the slope of a line?

A: The slope of a line is a measure of how steep the line is. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Q: How do I determine the midpoint of a line segment?

A: The midpoint of a line segment is the point that divides the line segment into two equal parts. To determine the midpoint, you can use the midpoint formula:

M = ((x1 + x2)/2, (y1 + y2)/2)

where M is the midpoint, and (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment.

Q: What is the equation of a line in slope-intercept form?

A: The equation of a line in slope-intercept form is:

y = mx + b

where m is the slope of the line, and b is the y-intercept.

Q: How do I graph a line in a coordinate plane?

A: To graph a line in a coordinate plane, you can use the slope-intercept form of the equation. You can also use the x-intercept and y-intercept to graph the line.

Conclusion

In this article, we answered some frequently asked questions about points in a coordinate plane. We hope that this article has provided you with a better understanding of the properties of points in a coordinate plane and how to work with them.

Additional Resources

If you are looking for more information about points in a coordinate plane, we recommend checking out the following resources:

Khan Academy: Coordinate Geometry
Mathway: Coordinate Geometry
Wolfram Alpha: Coordinate Geometry

We hope that this article has been helpful in your understanding of points in a coordinate plane. If you have any further questions, please don't hesitate to ask.