Cartesian Equation Calculator

Step-by-Step Guide to Using the Cartesian Equation Calculator

Introduction

The Cartesian Equation Calculator is a powerful tool designed to help you analyze the geometric relationship between two points. By inputting the coordinates of these points, you can determine various properties such as the slope, y-intercept, distance, and more.

Input Fields

Before you begin using the calculator, you’ll need to gather the necessary data. Specifically, this calculator requires the coordinates of two points in a Cartesian plane.

• X₁ Coordinate: Enter the x-coordinate of the first point. This field is required.
• Y₁ Coordinate: Enter the y-coordinate of the first point. This field is required.
• X₂ Coordinate: Enter the x-coordinate of the second point. This field is required.
• Y₂ Coordinate: Enter the y-coordinate of the second point. This field is required.

Calculating Results

Once you have entered all the required input data, the calculator will automatically compute the following properties:

• Slope (m): The slope of the line connecting the two points, calculated using the formula (y2 – y1) / (x2 – x1). This value is rounded to four decimal places.
• Y-Intercept (b): The y-intercept where the line crosses the y-axis, calculated using y1 – (((y2 – y1) / (x2 – x1)) * x1). This value is rounded to four decimal places.
• Line Equation: The equation of the line in the format y = mx + b, where m is the slope and b is the y-intercept. This is formatted to two decimal places.
• Distance Between Points: The straight-line distance between the two points, determined using the formula √((x2 – x1)² + (y2 – y1)²). This is displayed to four decimal places and includes the suffix ‘ units’.
• Midpoint X Coordinate: The x-coordinate of the midpoint between the two points, computed as (x1 + x2) / 2. This value is displayed to four decimal places.
• Midpoint Y Coordinate: The y-coordinate of the midpoint between the two points, computed as (y1 + y2) / 2. This value is displayed to four decimal places.
• Angle with X-Axis: The angle the line makes with the x-axis, calculated as atan2(y2 – y1, x2 – x1) * 180 / π. This angle is displayed to two decimal places and includes the suffix ‘°’.
• Perpendicular Slope: The slope of a line perpendicular to the one connecting the two points, calculated as -1 / slope. This value is rounded to four decimal places.

By following these steps and understanding the calculations involved, you’ll be able to effectively utilize the Cartesian Equation Calculator to gain insights into the geometric properties of lines and points.