Sketching Straight LinesUsing x & y intercepts | C cannot be equal to 0 | Gradient - intercept method | ax + by = c --> e.g 2x - 5y = 10 | y = mx + c | y = 0 when solving x | Horizontal Line | 2x - 0 = 10 | gradient = 0 | x = 5 | y = c | x = 0 when solving y | Vertical Line | 2(0) - 5y = 10 | gradient = undefined | -5y = 10 | x = a | y = 10/-5 | a --> x-intercept | y = -2 |
| | Finding the equation of a straight lineGradient + y-intercept | Gradient + a point (x1, y1) | 2 points (x1, y1) (x2, y2) | Distance between 2 points | Sub into equation | Sub into equation | 1st find m | Sub into equation | y = mx + c | y - y1 = m(x - x1) | m = y2 - y1/x2 - x1 | AB = √(x2 - x1)² + (y2 - y1)² | Example | Example | 2nd sub into equation | Example | c = 5 | m = -1 | m = 2 | (2, -0.5) | y - y1 = m(x - x1) | A = (3, -5) | B = (-2, 1) | y = -1x + 5 | y + 0.5 = 2(x - 2) | Example | AB = √(-2 - 3)² + (1 - -5)² | | | y + 0.5 = 2x - 4 | (-1, 4) , (5, 2) | AB = √(-5)² + 6² | | | y = 2x - 4.5 | m = 2 - 4/3 - (-1) | AB = √25 + 36 | | | | m = -2/4 --> -1/2 | AB = √61 | | | | y - 4 = -1/2(x - - 1) | | | | y - 4 = - 1/2x - 1/2 | | | | y = - 1/2x + 7/2 |
| | Middle point of a lineMiddle point of a line | Paralell Lines | Perpendicular Lines | Sub into equation - i.e / means divide | Sub into equation | Sub into equation | M = (x1 + x2/2, y1 + y2/2) | m1 = m2 | m1 x m2 = -1 or m2 = 1/m1 | Example | Example - 1st find m (gradient) | Example - 1st find m (gradient) | (3, 5) | (2, 7) | A (4, 13) | B (2, 9) | A (-4, 9) | B (2, -6) | M = 3 + 2/2, 5 + 7/2 | mAB = 9 - 13/2 - 4 | mAB = -6 - 9/2 - (-4) | M = (5/2, 12/2) | mAB = -4/-2 | mAB = -15/6 | M = (5/2, 6) | mAB = 2 | mAB = -5/2 | | | C (0, -10) | D (15, 0) | C (-5, 8) | D (10, 14) | | | mCD = 0 - (-10)/15 - 0 | mCD = 14 - 8/10 - (-5) | | | mCD = 10/15 | mCD = 6/15 | | | mCD = 2/3 | mCD = 2/5 | | | ∵ mAB ≠ mCB | 2nd | sub into m1 x m2 = -1 | | | ∴ not parralell | -5/2 x 2/5 = -1 | | | | -10/10 = -1 | | | | ∴ AB ⊥ CD |
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