1.3 Coordinate Geometry in the (x, y) Plane

• What is the Cartesian coordinate system used for?

  Locating points on a plane
• Negative y values move up along the y-axis.

  False
• What is the Cartesian coordinate system used for?

  Locating points on a plane
• To plot a point with coordinates (x, y), you first move along the y-axis and then the x-axis.

  False
• What formula is used to calculate the distance between two points in the Cartesian plane?

  \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}
• The x-coordinate of the midpoint is the average of the x-coordinates of the endpoints
• What does 'm' represent in the point-slope form of a line equation?

  Slope
• In the slope-intercept form, 'm' represents the slope
• In the point-slope form, (x₁, y₁) represents a point
• The point-slope form is used when the slope and a point are given.
• The simplified equation of a line with slope -1 passing through (1, 5) is $y =$$- x +$$6$.


  True
• The point where the x-axis and y-axis intersect is called the origin
• What are the coordinates of the origin in the Cartesian plane?

  (0, 0)
• What theorem is the distance formula derived from?

  Pythagorean theorem
• What is the formula for the midpoint between two points (x₁, y₁) and (x₂, y₂)?

  ((x₁ + x₂)/2, (y₁ + y₂)/2)
• The intersection of the x-axis and y-axis in the Cartesian coordinate system is called the origin
• The distance formula is derived from the Pythagorean theorem.


  True
• Match the form of a line equation with its components:

  Slope-Intercept Form ↔️ y = mx + b

  Point-Slope Form ↔️ y - y₁ = m(x - x₁)
• The y-intercept of a line is the point where the line crosses the y-axis
• The y-intercept in the slope-intercept form is represented by 'b'.


  True
• Match the line form with its equation:

  Slope-Intercept ↔️ $y =$$mx +$$b$

  Point-Slope ↔️ $y - y₁ =$$m(x - x₁)$
• What is the equation of a line with a slope of 2 and a y-intercept of 3 in slope-intercept form?

  y = 2x + 3</latex>
• Parallel lines have the same slope
• Match the property with the type of line:

  Parallel Lines ↔️ Same slope

  Perpendicular Lines ↔️ Negative reciprocal slope
• What is the equation of a circle with center (2, -3) and radius 5?

  (x - 2)² + (y + 3)² = 25</latex>
• Positive x values move left on the x-axis.

  False
• To plot a point, move along the x-axis by |x| units, where positive values move right
• The distance between two points (x₁, y₁) and (x₂, y₂) is √((x₂ - x₁)² + (y₂ - y₁)²)
• The midpoint lies exactly between two given points.

  True
• What are the coordinates of the origin in the Cartesian coordinate system?

  (0, 0)
• To plot a point with a positive x-coordinate, move along the x-axis to the right
• What is the formula for finding the midpoint between two points (x₁, y₁) and (x₂, y₂)?

  (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})
• In the equation y = mx + b, the variable 'm' represents the slope of the line.


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

  $y =$$mx +$$b$
• What is the point-slope form of a line equation?

  $y - y₁ =$$m(x - x₁)$
• The slope-intercept form is used when the slope and a point are given.

  False
• A line with a slope of -1 and passing through (1, 5) has the equation y - 5 = -1(x - 1)
• Perpendicular lines have slopes that are negative reciprocals of each other.


  True
• Which lines are perpendicular: $y =$$2x +$$3$ and $y =$$- 1 / 2x +$$4$?


  Perpendicular
• What is the slope of a line perpendicular to a line with slope m?

  -1/m</latex>