To find the coordinates of a point in a plane, you need two values: the $x$-coordinate and the $y$-coordinate. These values describe the position of the point relative to the origin (0, 0) on a Cartesian coordinate system. Here’s how you find and interpret coordinates:

1. Understanding the Cartesian Plane

• The Cartesian plane is divided into four quadrants by the $x$-axis (horizontal line) and the $y$-axis (vertical line).
• The coordinates of a point are written as $(x, y)$, where:
  • $x$ represents the horizontal distance from the origin.
  • $y$ represents the vertical distance from the origin.

2. Finding Coordinates on a Graph

• Step 1: Identify the point on the graph whose coordinates you want to find.
• Step 2: Draw a vertical line from the point to the $x$-axis to determine the $x$-coordinate.
• Step 3: Draw a horizontal line from the point to the $y$-axis to determine the $y$-coordinate.
• Step 4: Write the coordinates as $(x, y)$.

3. Finding Coordinates Algebraically

• If you have an equation of a line or a curve, you can substitute a value for $x$ into the equation to find the corresponding $y$ value (or vice versa). The resulting pair $(x, y)$ is the coordinate of a point on that line or curve.
• Example: For the line $y = 2x + 3$:
  • To find the coordinate where $x = 2$:
  • Substitute $x = 2$ into the equation: $y = 2(2) + 3 = 7$.
  • The coordinate is $(2, 7)$.

4. Special Cases:

• Origin: The coordinates of the origin are $(0, 0)$.
• Points on the Axes:
  • A point on the $x$-axis has coordinates $(x, 0)$.
  • A point on the $y$-axis has coordinates $(0, y)$.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. How do you find the midpoint between two points on a graph?
2. What is the distance formula, and how is it used to find the distance between two points?
3. How do you find the coordinates of the vertex of a parabola?
4. What are polar coordinates, and how do they differ from Cartesian coordinates?
5. How can you determine the equation of a line given two points on the line?

Tip: When reading coordinates on a graph, always move along the $x$-axis first (left or right) and then along the $y$-axis (up or down). This ensures you correctly identify the location of the point.