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Coordinates & Vectors

Gradients, reflections, position vectors and vector area.

24 lessons

1Gradient of a line through two pointsCoordinates & Vectors · Mr Wong · m = (y₂ − y₁) / (x₂ − x₁)2Section formula with position vectorsCoordinates & Vectors · Mr Wong · If P divides AB in m:n, then OP = (n·OA + m·OB) / (m + n)3Reflection across the axes and y = xCoordinates & Vectors · Mr Wong · reflection in x-axis: (x, y) → (x, −y)4Parallelogram area from two vectorsCoordinates & Vectors · Mr Wong · area = |x₁y₂ − x₂y₁| for a = (x₁, y₁), b = (x₂, y₂)5Distance between two pointsCoordinates & Vectors · Mr Wong · d = √[(x₂−x₁)²+(y₂−y₁)²]6Midpoint and section formula on a lineCoordinates & Vectors · Mr Wong · M = ((x₁+x₂)/2,(y₁+y₂)/2)7Equation of a line through two pointsCoordinates & Vectors · Mr Wong · m = (y₂−y₁)/(x₂−x₁)8Parallel and perpendicular gradientsCoordinates & Vectors · Mr Wong · parallel: m₁=m₂9Area of a triangle from coordinatesCoordinates & Vectors · Mr Wong · area = ½|det form|10Circle equation from centre and radiusCoordinates & Vectors · Mr Wong · (x−h)²+(y−k)²=r²11Intersection of a line and a circleCoordinates & Vectors · Mr Wong · discriminant >0 two points12Vector addition as a parallelogramCoordinates & Vectors · Mr Wong · a + b = diagonal13Position vectors and midpointsCoordinates & Vectors · Mr Wong · OM = (a+b)/214Rotation by 90° about the originCoordinates & Vectors · Ms Ho · 90° ACW: (x,y)→(−y,x)15Enlargement from a centreCoordinates & Vectors · Ms Ho · X′ = C + k(X − C)16Locus: perpendicular bisectorCoordinates & Vectors · Mr Wong · |PA|=|PB| ⇒ P on perp. bisector of AB17Proving collinearity with vectorsCoordinates & Vectors · Mr Wong · AB = k AC18Dot product and right anglesCoordinates & Vectors · Mr Wong · a · b = |a||b|cos θ19Parametric equation of a lineCoordinates & Vectors · Mr Wong · r = a + t d20Translation by a vectorCoordinates & Vectors · Ms Ho · (x,y) → (x+a,y+b)21Coordinate proof that a quadrilateral is a parallelogramCoordinates & Vectors · Mr Wong · midpoint AC = midpoint BD22Shortest path via a mirror lineCoordinates & Vectors · Ms Ho · reflect → straight line → intersect mirror23Gradient as tan of the inclinationCoordinates & Vectors · Mr Wong · m = tan θ24Dividing a segment in a vector ratioCoordinates & Vectors · Mr Wong · p = (n a + m b)/(m+n)