Find Quadrant of the Coordinate Point

Coordinates play a fundamental role in arithmetic and diverse clinical disciplines. They are important for representing the place of factors in space, and knowledge of the relationships among these factors is critical. In this newsletter, we are able to delve into the concept of quadrant class for coordinates within the context of the R programming language. Quadrant classification is an essential idea in Cartesian coordinate systems, and it could be used to categorize factors based totally on their relative function to the origin.

Concepts Related to the Topic

Quadrant Classification for Coordinates has some following concepts that are described as follows.

Cartesian Coordinate System

The Cartesian coordinate device, advanced by way of René Descartes, is a two-dimensional plane represented with the aid of perpendicular axes – the x-axis and the y-axis. This device allows us to represent factors in a plane by using pairs of real numbers (x, y), in which ‘x’ represents the horizontal role along the x-axis and ‘y’ represents the vertical role alongside the y-axis. The intersection of those axes is referred to as the beginning, and its miles are denoted as (0,0).

Quadrants

Quadrants are the four regions created by way of the Cartesian coordinate machine. Each quadrant is described by using its function relative to the origin, and it has a unique set of characteristics:

• Quadrant I: Points in this quadrant have positive x and y coordinates. This quadrant is located inside the higher right place of the coordinate plane.
• Quadrant II: Points on this quadrant have negative x and positive y coordinates. It is located in the upper left area of the plane.
• Quadrant III: Points on this quadrant have negative x and y coordinates and are located within the lower left place of the plane.
• Quadrant IV: Points in this quadrant have positive x and negative y coordinates and are located within the lower right place of the plane.

PLot Quadrants using R

R

library(ggplot2)

ggplot() +
  labs(title = "Coordinate System") +
  geom_vline(xintercept = c(0, 5, -5), color = c('black', 'gray', 'gray')) +
  geom_hline(yintercept = c(0, 5, -5), color = c('black', 'gray', 'gray')) +
  annotate("text", x = 2, y = 2, label = "Quadrant I", color = 'red') +
  annotate("text", x = -2, y = 2, label = "Quadrant II", color = 'green') +
  annotate("text", x = -2, y = -5, label = "Quadrant III", color = 'blue') +
  annotate("text", x = 2, y = -2, label = "Quadrant IV", color = 'pink') +
  xlim(c(-5, 5)) +
  ylim(c(-5, 5)) +
  theme_minimal()

Output:

coordinate System

Steps Needed

To classify coordinates into quadrants in R, you want to observe these steps:

• Input Coordinates: The first step is to attain the entered coordinates within the shape of (x, y) pairs. These can be provided as a list, vector, or statistics frame, relying for your records supply.
• Calculate Quadrants: Next, calculate the quadrant for every set of coordinates. This can be done the use of conditional statements, where you evaluate the signs and symptoms of the x and y values to decide the quadrant.
• Assign Quadrant Labels: Once you’ve got decided the quadrant for every point, assign labels (I, II, III, IV) to signify which quadrant every point falls into.
• Visualize the Results: You can create visualizations to symbolize the factors in their respective quadrants, offering a clean illustration of the statistics.

Quadrant Classification of Random Points

Let’s start with a easy instance where we’ve a set of random points in R, and we need to categorise them into quadrants.

R

# Generate random coordinates
set.seed(123)  # Set seed for reproducibility
n_points <- 10
x <- runif(n_points, min = -10, max = 10)
y <- runif(n_points, min = -10, max = 10)

# Create a data frame with coordinates
coordinates <- data.frame(x, y)

# Calculate quadrant
coordinates$quadrant <- ifelse(coordinates$x > 0,
                               ifelse(coordinates$y > 0, "I", "IV"),
                               ifelse(coordinates$y > 0, "II", "III"))

# Display the result
print(coordinates)

Output:

            x          y quadrant
1  -4.2484496  9.1366669       II
2   5.7661027 -0.9333169       IV
3  -1.8204616  3.5514127       II
4   7.6603481  1.4526680        I
5   8.8093457 -7.9415063       IV
6  -9.0888700  7.9964994       II
7   0.5621098 -5.0782453       IV
8   7.8483809 -9.1588093       IV
9   1.0287003 -3.4415856       IV
10 -0.8677053  9.0900730       II

In this example, we generated random points with coordinates between -10 and 10, calculated their respective quadrants using conditional statements, and assigned quadrant labels.

Quadrant Classification with Plot

To visualize the points in their respective quadrants, we can create a scatter plot.

R

# Load the ggplot2 library
library(ggplot2)

# Create a scatter plot with color-coded quadrants
ggplot(coordinates, aes(x = x, y = y)) +
  geom_point(size = 3) +
  labs(title = "Quadrant Classification for Coordinates Points") +
  geom_vline(xintercept = c(0, 15, -15), color = c('black', 'gray', 'gray')) +
  geom_hline(yintercept = c(0, 5, -5), color = c('black', 'gray', 'gray')) +
  annotate("text", x = 7, y = 7, label = "Quadrant I", color='red') +
  annotate("text", x = -7, y = 7, label = "Quadrant II", color='green') +
  annotate("text", x = -7, y = -7, label = "Quadrant III", color='blue') +
  annotate("text", x = 7, y = -7, label = "Quadrant IV", color='pink')+
  theme_minimal()

Output:

Quadrant Classification for Coordinates Points

In this situation, we used the ggplot2 package deal to create a scatter plot with points shade-coded with the aid of quadrant. This visualization makes it easy to apprehend the distribution of points in each quadrant.

Quadrant Classification of Known Points

Let’s don’t forget a state of affairs wherein we’ve a dataset of known points and we want to categorise them into quadrants.

R

# Load the ggplot2 package
library(ggplot2)

# Sample coordinates
x <- c(1, -2, -3, 4, 5)
y <- c(2, 3, -4, -5, 6)

# Initialize vectors to store quadrant information
quadrant <- character(length(x))

# Classify coordinates into quadrants
for (i in 1:length(x)) {
  if (x[i] > 0 && y[i] > 0) {
    quadrant[i] <- "Quadrant I"
  } else if (x[i] < 0 && y[i] > 0) {
    quadrant[i] <- "Quadrant II"
  } else if (x[i] < 0 && y[i] < 0) {
    quadrant[i] <- "Quadrant III"
  } else if (x[i] > 0 && y[i] < 0) {
    quadrant[i] <- "Quadrant IV"
  } else {
    quadrant[i] <- "Origin"
  }
}

# Create a data frame to store the results
coordinates_df <- data.frame(x, y, quadrant)

coordinates_df

Output:

   x  y     quadrant
1  1  2   Quadrant I
2 -2  3  Quadrant II
3 -3 -4 Quadrant III
4  4 -5  Quadrant IV
5  5  6   Quadrant I

We define two vectors x and y, which represent the x and y coordinates of data points. You’ve provided sample values for these coordinates.

• create an empty character vector named quadrant with the same length as the x and y vectors. This vector will be used to store the quadrant information for each data point.
• iterate through each data point using a for loop. For each data point at index i, you examine its x and y coordinates to determine its quadrant:
• If both x and y are positive, it’s assigned to “Quadrant I.”
• If x is negative and y is positive, it’s assigned to “Quadrant II.”
• If both x and y are negative, it’s assigned to “Quadrant III.”
• If x is positive and y is negative, it’s assigned to “Quadrant IV.”
• If none of the above conditions are met (both x and y are zero), it’s assigned to “Origin.”
• You store the quadrant classification for each data point in the quadrant vector.

Visualize the Quadrant Coordinates

R

# Create a scatter plot with color-coded quadrants
ggplot(coordinates_df, aes(x = x, y = y)) +
  geom_point(size = 2) +
  labs(title = "Quadrant Classification for Coordinates Points") +
  geom_vline(xintercept = 0) +
  geom_hline(yintercept = 0) +
  annotate("text", x = 3, y = 5, label = "Quadrant I", color='red') +
  annotate("text", x = -2, y = 5, label = "Quadrant II", color='green') +
  annotate("text", x = -2, y = -5, label = "Quadrant III", color='blue') +
  annotate("text", x = 3, y = -5, label = "Quadrant IV", color='pink')+
  theme_minimal()

Output:

Quadrant Classification for Coordinates Points

we use the ggplot2 package to create a scatter plot of the coordinates. We map the x and y coordinates to the plot’s x and y aesthetics, and we use the color aesthetic to differentiate points by their quadrant classification. We also add labels for each point’s quadrant and set the plot’s title and theme.