math

    Cards (40)

    • How do parallel lines behave?
      They never meet
    • What is the gradient of parallel lines?
      They have the same gradient
    • What defines perpendicular lines?
      They cross at a right angle
    • What is the angle at which perpendicular lines intersect?
      90°
    • What happens to the gradient of a line that is perpendicular to another?
      It must be negative
    • What is the gradient of the purple line perpendicular to y = 2x + 1?
      -1/2
    • How do you calculate the gradient of the purple line?
      Change in Y over change in X
    • What is the gradient of the line perpendicular to y = 3x + 2?
      -1/3
    • What is the relationship between the gradients of perpendicular lines?
      • They are negative reciprocals of each other
      • Their product equals -1
    • What is the reciprocal of 2?
      1/2
    • What is the reciprocal of 3?
      1/3
    • What is the reciprocal of a fraction like 2/3?
      3/2
    • How do you find the reciprocal of a decimal like 0.9?
      Convert to fraction, then flip
    • How do you show two lines are perpendicular?
      Multiply their gradients to get -1
    • What do you conclude if the product of two gradients is -1?
      The lines are perpendicular
    • What do you conclude if the product of -2/3 and 3/2 is -1?
      The lines are perpendicular
    • How do you determine if two lines are perpendicular?
      Multiply their gradients to get -1
    • How do you find the gradient of L2 if L1's gradient is -4?
      Take the negative reciprocal
    • What form do we write the equation of L2?
      y = mx + C
    • How do you find the gradient of L2 from L1's gradient of 34\frac{3}{4}?

      Take the negative reciprocal
    • What is the gradient of L2 if L1's gradient is 34\frac{3}{4}?

      -43\frac{4}{3}
    • How do you find C using the point (6, -1)?
      Substitute into the equation
    • What is the formula to find the gradient between two coordinates?
      \(\frac{y_2 - y_1}{x_2 - x_1}\)
    • How do you find the gradient of line AB using coordinates A(1, 5) and B(3, 6)?
      Substitute into the gradient formula
    • What is the gradient of line AB from the coordinates given?
      12\frac{1}{2}
    • What is the gradient of the line perpendicular to AB?
      -2
    • What is the equation of the line perpendicular to AB?
      y = -2x + C
    • How do you find C using the point (1, 5)?
      Substitute into the equation
    • What is the value of C after substituting (1, 5)?
      -3
    • What is the final equation of the line perpendicular to AB?
      y = -2x - 3
    • What is the gradient of line AB in the last example?
      52\frac{5}{2}
    • How do you find the gradient of the line perpendicular to AB?
      Take the negative reciprocal
    • What is the gradient of the line perpendicular to AB?
      -25\frac{2}{5}
    • How do you write the equation of the line perpendicular to AB?
      y = -25\frac{2}{5}x + C
    • How do you find C using the point (10, -2)?
      Substitute into the equation
    • What is the value of C after substituting (10, -2)?
      2
    • What is the final equation of the line perpendicular to AB?
      y = -25\frac{2}{5}x + 2
    • What are the steps to find the equation of a line perpendicular to another line given a point?
      1. Find the gradient of the first line.
      2. Calculate the negative reciprocal for the perpendicular line's gradient.
      3. Use the point to find the Y-intercept (C).
      4. Write the equation in the form y = mx + C.
    • What are the key concepts in determining if two lines are perpendicular?
      • Calculate gradients of both lines.
      • Their product must equal -1.
    • What is the process for finding the gradient from two coordinates?
      • Use the formula: y2y1x2x1\frac{y_2 - y_1}{x_2 - x_1}
      • Substitute the coordinates into the formula.
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