Straight line

• What is the gradient of a line?

  Slope of the line
• How do you determine if two lines are perpendicular?

  If the product of their gradients is -1
• What does it mean if two lines are collinear?

  They lie on the same straight line
• How do you find the gradient between two points A and B?

  $\frac{y_2 - y_1}{x_2 - x_1}$
• What is the relationship between the gradients of two parallel lines?

  Their gradients are equal
• How do you find the angle a line makes with the x-axis using its gradient?

  $\theta =$$\tan^{-1}(m)$
• What is a perpendicular bisector?

  A line that cuts another line segment into two equal parts at 90 degrees
• What is a median in geometry?

  A line segment from a vertex to the midpoint of the opposite side
• What is an altitude in geometry?

  A perpendicular line from a vertex to the opposite side
• How do you find the midpoint of a line segment?

  $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$
• What is the gradient of a line perpendicular to another line with gradient $m$?


  $-\frac{1}{m}$
• How do you form the equation of a line given its gradient and a point it passes through?

  $y - y_1 =$$m(x - x_1)$
• What are the key steps to find the equation of a line?

  1. Find the gradient (m)
  2. Identify a point on the line (x₁, y₁)
  3. Use the point-slope form: $y - y_1 =$$m(x - x_1)$
• What are the differences between median, altitude, and perpendicular bisector in a triangle?

  • Median: Connects vertex to midpoint of opposite side
  • Altitude: Perpendicular from vertex to opposite side
  • Perpendicular Bisector: Perpendicular line that bisects a side
• How do you determine if three points are collinear?

  1. Find gradients between pairs of points (e.g., AB and BC)
  2. If gradients are equal, points are collinear
• What are the properties of perpendicular lines?

  • Their gradients are negative reciprocals
  • They intersect at 90 degrees
  • Product of their gradients is -1