Flashcards · 4MA1 · Topic 5

Vectors and transformation geometry flashcards

13 cards on Topic 5, subtopics 5.1 to 5.2. Pick a subtopic or study them all.

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Vector and scalarHigher: Vector: a quantity with magnitude and direction. Scalar: a quantity with magnitude only.
Resultant vectorHigher: The single vector with the same effect as two or more vectors followed in turn.
Modulus of a vector, and |(−9, 12)|Higher: The magnitude (length) of a vector, written |a|: |(x, y)| = √(x² + y²). |(−9, 12)| = √(81 + 144) = 15
A is (1, 3) and B is (4, −1). Find →AB.Higher: →AB = →OB − →OA ("end minus start") = (4 − 1, −1 − 3) = (3, −4).
Parallel vectorsHigher: One is a scalar multiple of the other. 6a − 9b = 3(2a − 3b), so they are parallel.
Parallel vectors and collinear points: what is the difference?Higher: Parallel needs a scalar multiple only; collinear also needs a shared point.
P is on AB with AP : PB = 3 : 1. Write →AP in terms of →AB.Higher: →AP = (3/(3 + 1))→AB = (3/4)→AB.

What do you give to describe fully each transformation?: Rotation: centre and angle (anticlockwise +, clockwise −). Reflection: the mirror line. Translation: the column vector. Enlargement: centre and scale factor.
Rotations of (x, y) about the origin: +90° (anticlockwise): (−y, x). −90° (clockwise): (y, −x). 180°: (−x, −y).
Reflect (5, −2) in y = x, and in x = 1: In y = x: swap the coordinates, (−2, 5). In x = 1: (2 × 1 − 5, −2) = (−3, −2).
Which transformations give congruent images and which give similar images?: Rotation, reflection and translation give congruent images; enlargement gives similar images.
A side of 6 cm maps to 2 cm, the same way round. Describe the transformation.: Enlargement, scale factor 2 ÷ 6 = 1/3, plus its centre. A smaller image is still called an enlargement; 4MA1 uses positive scale factors only.
How do you find a translation vector from an object and its image?: Image minus object, for x and then y. Object minus image reverses both signs.