Topic 2: Vectors and Translations – Sample Activity

Context

Mrs Opio wished to travel late in the evening from town A to town C using a short route. Unfortunately, there was a heavy storm and a big tree fell across the short route. There are six towns A, B, C, D, E and F. The distance between A and B is 60 km. The distance between B and C is 50 km, between A and C is 100 km, between C and E is 125 km, between A and F is 20 km and between F and E is 30 km.

Resources
Knowledge of vectors.
Task
As a navigator, advise Mrs Opio on how she can reach her destination.

Topic Summary
In this topic, you have learnt that:

• a translation moves every point in a figure the same distance in the
  same direction.
• the size, the shape and the orientation of the image are the same as that of the original object. Same orientation means that the object and image are facing the same direction.
• vectors are used to represent a quantity that has both a magnitude and a direction.
• vectors used with translations may also be called displacement vectors or translation vectors.
• scalars are quantities that are fully described by a magnitude (or numerical value) alone.
• a translation can be represented by a column vector where x is the number of units to move right or left along the x-axis and y is the number of units to move up or down along the y-axis.
• a vector is represented by a directed line segment, a segment with an arrow at one end indicating the direction of movement. Unlike a geometric ray, a directed line segment has a specific length.
• the direction of the vector is indicated by an arrow pointing from the tail (the initial point) to the head (the terminal point). If the tail is at point A and the head is at point B, the vector from A to B can be written as AB.