How to work for this one? Given the corner points of a triangle $(x_1, y_1), (x_2, y_2), (x_3, y_3)$, write a function to compute the area.**Hint:** The area of the triangle with corner points $(0, 0), (x_1, y_1), (x_2, y_2)$ is \[\frac{|x_1 \cdot y_2 - x_2 \cdot y_1|}{2}\]To use this formula, you shift the given triangle so that one of its corners falls on the origin. This shift does not change the area. The corner points of the triangle shifted by $(x, y)$ are $(x_1 - x, y_1 - y), (x_2 - x, y_2 - y), (x_3 - x, y_3 - y)$.### geometry.cpp```cpp#include using namespace std;/** * Computes the area of a triangle. * @param x1 the x-coordinate of the first corner * @param y1 the y-coordinate of the first corner * @param x2 the x-coordinate of the second corner * @param y2 the y-coordinate of the second corner * @param x3 the x-coordinate of the third corner * @param y3 the y-coordinate of the third corner * @return the area of the triangle */double area(double x1, double y1, double x2, double y2, double x3, double y3){ // ...}```**Explanation:** This code snippet defines a function for calculating the area of a triangle given the coordinates of its corners. You supply the function with the x and y coordinates of each corner, and it returns the computed area. The formula utilizes a mathematical transformation that allows for computing the area of shifted triangles without needing complex trigonometric calculations.

For given coordinates of the three sides of the triangle, when we shifted side to falls on the…

Answered: Given the corner points of a triangle…

Engineering

Computer Science

Given the corner points of a triangle (x, y,), (x2, y2), (X3, Y3), write a function to compute the area.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

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How to work for this one?

Given the corner points of a triangle $(x_1, y_1), (x_2, y_2), (x_3, y_3)$, write a function to compute the area.

**Hint:** The area of the triangle with corner points $(0, 0), (x_1, y_1), (x_2, y_2)$ is

\[
\frac{|x_1 \cdot y_2 - x_2 \cdot y_1|}{2}
\]

To use this formula, you shift the given triangle so that one of its corners falls on the origin. This shift does not change the area. The corner points of the triangle shifted by $(x, y)$ are $(x_1 - x, y_1 - y), (x_2 - x, y_2 - y), (x_3 - x, y_3 - y)$.

### geometry.cpp

```cpp
#include <cmath>
using namespace std;

/**
* Computes the area of a triangle.
* @param x1 the x-coordinate of the first corner
* @param y1 the y-coordinate of the first corner
* @param x2 the x-coordinate of the second corner
* @param y2 the y-coordinate of the second corner
* @param x3 the x-coordinate of the third corner
* @param y3 the y-coordinate of the third corner
* @return the area of the triangle
*/
double area(double x1, double y1, double x2, double y2, double x3, double y3)
{
// ...
}
```

**Explanation:** This code snippet defines a function for calculating the area of a triangle given the coordinates of its corners. You supply the function with the x and y coordinates of each corner, and it returns the computed area. The formula utilizes a mathematical transformation that allows for computing the area of shifted triangles without needing complex trigonometric calculations.

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