Geometry
Geometry is a branch of mathematics that deals with the deduction of the properties, measurements, and relationships of points, lines, angles and figures in space from their defining condition by means of certain assumed properties of space. So far, we have been focusing on algebraic geometry and vectors, but over the course of the year we will cover a much wider scale of subjects.
The following assignments and pictures are things that we have been working on throughout the course of the whole first semester. Two of the main things were rotations and coordinate planes. Below are examples of work that we did in class.
Assignment #4
2. I have been observing the motion of a bug that is crawling on my graph paper. When I started watching, it was at the point (1,2). Ten seconds later it was at (3,5). Another ten seconds later it was at (5,8). After another ten seconds it was at (7,11).
(a) Draw a picture that illustrates what is happening.
(b) Write a description of any pattern you notice. What assumptions are you making?
(c) Where was the bug 25 seconds after I started watching it?
(d) Where was the bug 26 seconds after I started watching it
2. I have been observing the motion of a bug that is crawling on my graph paper. When I started watching, it was at the point (1,2). Ten seconds later it was at (3,5). Another ten seconds later it was at (5,8). After another ten seconds it was at (7,11).
(a) Draw a picture that illustrates what is happening.
(b) Write a description of any pattern you notice. What assumptions are you making?
(c) Where was the bug 25 seconds after I started watching it?
(d) Where was the bug 26 seconds after I started watching it
Assignment #10
4. A bug is moving along the line 3x+4y=12 with constant speed 5 units per second. Find parametric equations to describe the line 3x+4y=12. Use your equations to find coordinates for the point that is three-fifths of the way from (4,0) to (0,3) by substituting T=3/5. By calculating some distances, verify that you have the correct point.
4. A bug is moving along the line 3x+4y=12 with constant speed 5 units per second. Find parametric equations to describe the line 3x+4y=12. Use your equations to find coordinates for the point that is three-fifths of the way from (4,0) to (0,3) by substituting T=3/5. By calculating some distances, verify that you have the correct point.