Section 7: Circles and Ellipses
In the last section, we saw that the equation of a line \[
y = y_A + m(x  x_A)
\] can be obtained by considering a fixed point \(A(x_A,y_A)\) on the line and another general point \
(P(x,y)\). This equation restricts \(P\)
Section 5: Introduction to Analytic Geometry
5.1: What is analytic geometry?
Analytic geometry is the study of geometry by placing plane geometric figures (points, lines, circles, etc)
on coordinate axes. For example, we can analyze a triangle like the on
Section 6: Lines
6.1: Slope of a line
The slope of a line is defined as the change in the \(y\)direction (rise) divided by the change in the \(x\)direction. It is a measure of the steepness of a line. The following gives the formula for finding the slope
Section 3: Angles and Triangles
3.1: Angular measurement
Consider a pair of parallel lines crossed by a straight line.
As we know, right angles are \(90^\circ\). The sum of all angles on a straight line is \(180^\circ\), e.g, \(a
+ c = 180^\circ\). We als
Section 2: Length, Area and Volume
2.1: Perimeter, Area and Volume
The perimeter of a plane geometric figure is the total distance around the boundary of the figure. The
perimeter of a circle is also called the circumference.
The following table lists the
Section 1: Ratios and rates
5.1: Ratio
The quotient \(\dfraccfw_acfw_b\) is called the ratio of \(a\) to \(b\). This ratio is sometimes written as \(a:b\).
Example 1
A paint that has a specific tone of blue color can be made by mixing 3 parts of normal bl
Sunday, September 27, 2015
22:17
Find the length of a rod that is required to make the following frame.
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Friday, September 25, 2015
12:30
A ball bearing sits between two metal grooves as shown below. If the distance between the
vertices of the grooves is 5 mm, what must the radius of the ball bearing be?
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Wednesday, September 23, 2015
08:24
A truss structure is shown on the right.
Find the length x.
20150923 Trigonometry Page 1

A piston and rod assembly is shown below. Find the maximum angle between the cylinder and
the piston rod.
20150923 Trigonome
Monday, September 21, 2015
10:32
Find the area of this shape.
How about
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etc
A cylinder is supported by a cable and a smooth incline plane shown on the left with a freebody diagram on the right.
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A cylinder is sup
Thursday, September 17, 2015
22:33
If an alloy containing 30% silver by mass (called a 30%
alloy) is mixed with a 55% alloy to get 800 kg of 40%
alloy, how much of each of the alloys must be added?
20150918 Ratios and Rates Page 1
An athlete ran for 4 k