MODULE IV VOCABULARY PART I

MODULE IV Module IV more than any module thus far, will overlap with others. Module IV is called simply, “Triangles” and we have already intensively discussed these!

MODULE IV When I transform a figure it is important to discuss what is preserved. To say something is preserved in math is to say that it stays the same through a transformation.

MODULE IV The features that can be preserved are – Distance – Angle Measure – Orientation – Area

MODULE IV Distance is the measure of the length between points of a figure. Angle measure is the measure of the angles.

MODULE IV Orientation is the order the points of the figure fall in. For instance, the orientation of the figures below are not the same. A C B C’ B’ A’

MODULE IV Area refers to the size of the area. What transformation have we done that would NOT preserve area? What transformations would preserve area?

MODULE IV Lastly today, we will discuss horizontal and vertical stretches. In doing so, we will examine how the area of such figures change.

MODULE IV When I am horizontally stretching something, I am essentially changing ONLY the x element by a given scale factor. When I am vertically stretching something, I am essentially changing ONLY the y element by a given scale factor.

MODULE IV So say I started with the figure below.

MODULE IV The coordinates that create this triangle are (2, 8), (4, 0) and (0, 0). If I am asked to horizontally stretch this figure, by a factor of 2.

MODULE IV My points would now be (4, 8), (8, 0) and (0, 0)

MODULE IV See? Each x value is multiplied by the scale factor. What if I was “stretching” my figure by a scale factor of ½? What if I was stretching my figure vertically?

MODULE IV How do the area’s of these figures compare? Well, that depends on how many dimensions are changing and by how much. Say we were dealing with our last stretch.

MODULE IV The original triangle had a base of 4 and a height of 8. Therefore its area was 16 units². The new triangle has a base of 8 and a height of 8. So it’s new area is 32.

MODULE IV The area is multiplied by each dimension’s scale factor. If there is a horizontal stretch of 2 and a vertical stretch of 4, the area change will be 8. Today, you’ll be asked to do all these things.