## Questions and Answers

What is the point of intersection of the x-axis and the y-axis called?

What is the formula to find the distance between two points (x1, y1) and (x2, y2)?

What is the equation of a circle with center (h, k) and radius r?

What is the slope of a line passing through two points (x1, y1) and (x2, y2)?

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

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In which quadrant do the points with x > 0 and y > 0 lie?

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## Study Notes

### What is Coordinate Geometry?

- Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes and their properties using algebraic and analytic methods.
- It involves the use of coordinates (x, y) to locate points in a plane and to define geometric shapes.

### Coordinate Plane

- A coordinate plane is a two-dimensional plane formed by two perpendicular lines, the x-axis and the y-axis.
- The x-axis is the horizontal line, and the y-axis is the vertical line.
- The point of intersection of the two axes is called the origin (0, 0).

### Quadrants

- The coordinate plane is divided into four quadrants:
- Quadrant I: x > 0, y > 0
- Quadrant II: x < 0, y > 0
- Quadrant III: x < 0, y < 0
- Quadrant IV: x > 0, y < 0

### Distance Formula

- The distance between two points (x1, y1) and (x2, y2) is given by: √((x2 - x1)^2 + (y2 - y1)^2)

### Midpoint Formula

- The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by: ((x1 + x2)/2, (y1 + y2)/2)

### Slope Formula

- The slope of a line passing through two points (x1, y1) and (x2, y2) is given by: (y2 - y1) / (x2 - x1)

### Equations of Lines

- The equation of a line can be written in various forms:
- Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept
- Point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope
- Standard form: Ax + By = C, where A, B, and C are constants

### Circles

- The equation of a circle with center (h, k) and radius r is given by: (x - h)^2 + (y - k)^2 = r^2

### Coordinate Geometry

- Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes and their properties using algebraic and analytic methods.
- It involves the use of coordinates (x, y) to locate points in a plane and to define geometric shapes.

### Coordinate Plane

- A coordinate plane is a two-dimensional plane formed by two perpendicular lines, the x-axis and the y-axis.
- The x-axis is the horizontal line, and the y-axis is the vertical line.
- The point of intersection of the two axes is called the origin (0, 0).

### Quadrants

- The coordinate plane is divided into four quadrants.
- Quadrant I: x > 0, y > 0
- Quadrant II: x < 0, y > 0
- Quadrant III: x < 0, y < 0
- Quadrant IV: x > 0, y < 0

### Distance Formula

- The distance between two points (x1, y1) and (x2, y2) is given by: √((x2 - x1)^2 + (y2 - y1)^2)

### Midpoint Formula

- The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by: ((x1 + x2)/2, (y1 + y2)/2)

### Slope Formula

- The slope of a line passing through two points (x1, y1) and (x2, y2) is given by: (y2 - y1) / (x2 - x1)

### Equations of Lines

- The equation of a line can be written in various forms.
- Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept
- Point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope
- Standard form: Ax + By = C, where A, B, and C are constants

### Circles

- The equation of a circle with center (h, k) and radius r is given by: (x - h)^2 + (y - k)^2 = r^2

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## Description

Learn about the fundamentals of coordinate geometry, including the coordinate plane and its components, the x-axis and y-axis.