Cheatography

# Co-Ordinate Geometry & Simultaneous Equations Cheat Sheet by Ebrahim.O

Cheat Sheet for Co-Ordinate Geometry & Simultaneous EquationsEnjoy :)

### Sket­ching Straight Lines

 Using 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 line

 Gradient + 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 line

 Middle 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