April 26, 2017
notes 13.3
Chapter 13-Coordinate Geometry extended.
13.1 Graphing equations
We have already studied equations of the line. There are several
forms:
slope-intercept y = mx + b
point-slope
y - y1=m(x - x1)
standard or general ax + by + c = o
Intercept x/a + y/b = 1
Two-point y - y1 = y2 - y1
x - x1
x2 - x1
April 26, 2017
notes 13.3
Write the equation of the line that passes through a vertex
of
ABC and the midpoint of side AC. A(-3,2) B(7,4) C(5,-8).
What is the name of this line? If you repeated this process from
all vertices, what would occur.
notes 13.3
April 26, 2017
How would you describe the set of points equidistant from a
given point in the plane?
Consider the example: Write an equation that describes the
set of points that are 6 units from P(2,4).
notes 13.3
April 26, 2017
What does the equation x^2 - 4x + y^2 + 6y = 12
represent?
Line QR is tangent to circle P. Circle P has center at (1, 1) with
radius 5. Q is located at (4, 5) Write the equation for line QR
April 26, 2017
notes 13.3
HW ch 13
13. 1 P. 607 #5,7,10,12,14,15,21-24
13.2 P. 615 #7-16, 19-24, 27
13.3 P. 620 #5-12, 14, 15
13.4 P. 624 #5 ab, 6-9
13.6 P. 635 #3ab,4-7, 8ac, 9ac ,11ac,13-18
13.7 P. 639 #2-20,22-25,27,28
April 26, 2017
notes 13.3
13.2 equations of lines
FInd the orthocenter for the triangle BCH if B(2,1), C(8, 7)
and H( 6, -3)
Does the point (2, -5) lie on the line whose slope is -4/5 and
whose x-intercept is -4?
notes 13.3
April 26, 2017
How would you find the centre of a circle if you knew that the
points (5, -3), (3, 3) and (19, 11) all lie on the circle?
(HINT: think circumcenter)
If you reflect the point (-3, 4) over the x-axis, what is its image?
what if you reflect (-3, 4) over the y-axis?
How about over the line y=x ?
April 26, 2017
notes 13.3
Reflect the line y= -1/2x +3
over the y-axis
notes 13.3
April 26, 2017
Find an equation of the reflection of the line y =2/3x +2 over the
x-axis.
over the y-axis
over the line y = x
April 26, 2017
notes 13.3
Find the equation of the tangent line to the
circle with equation x^2 -8x +y^2 +8y=201 at
the point (9, 8)
notes 13.3
April 26, 2017
notes 13.3
April 26, 2017
13.3 Systems of equations
What does a system of equations look like? What does it mean
to solve a system of equations?
There are several methods to use to solve a system of equations:
*substitution
*elimination
*graphing
*matrices (linear only)
can you give an example of each of these types and/or
explain how to apply the methods.
April 26, 2017
notes 13.3
Use substitution to determine the points of intersection for
x^2 + y^2 = 144
x= 5
Use elimination to determine the points of intersection for
2x - 3y = 6
4x +5y =11
Use matrices to determine the points of intersection for
2x +21y = 7
-4x - 13y = 4
Use graphing to determine the points of intersection for
x^2 + y = 36
2x^2 + 4x - 3 = y
April 26, 2017
notes 13.3
An interesting application of systems....
Find the distance between the parallel lines
y= 3x + 5
y = 3x -2 and
April 26, 2017
notes 13.3
13.4 Graphing Inequalities
To graph an inequality, pretend that the inequality is actually an
equation and use the equation to create a boundary.
Next decide what points make the inequality true, i.e., test
coordinates.
Shade the appropriate region that satisfies the inequality.
graph y > -3x +4
April 26, 2017
notes 13.3
Graph y < -2x -5 and y > 3/2x -7
Graph y <
x-4
April 26, 2017
notes 13.3
Graph the solution set for y < x^2 +2 and y > -1
graph x^2 + y^2 < 36
y>
x-1
notes 13.3
Work in small groups and investigate #9 on page 625 of your
book. This is a beginners look at calculus!
April 26, 2017
notes 13.3
April 26, 2017
13.6 CIRCLES
Recall the model for the equation of a circle:
r^2 = (x-h)^2 + (y-k)^2 where r represents the radius and
(h, k) represents the coordinates of the center.
Let the center of a circle be ( -2, 4) and the radius is 5. Find the
equation of the circle.
notes 13.3
April 26, 2017
The equation x^2 + 4x + y^2 - 6y = 12 represents a circle. Find the
center and the radius.
So...how do you do this? Let's think about the following situations:
x^2 +4x +4 = (x + ? )^2
x^2 - 10x + 25 = (x + ? )^2
x^2 +8x + ? = (x + 4)^2
notes 13.3
April 26, 2017
Write the equation of the circle with center at (-1, 5) and
passes through the point (4, 17)
Find the equation of the tangent line to the circle with equation
x^2 -2x +y^2 + 6y =15 at the point (-3, -6)
April 26, 2017
notes 13.3
Find the area and
(8, 2)
(10, 0)
circumference of the circle
April 26, 2017
notes 13.3
13.7 Coordinate Geometry Practice
What is the area of
the shaded region
(-6,2)
(-6,-4)
(2,2)
(2,-4)
April 26, 2017
notes 13.3
Point (-2, 4) lies on circle A. The center of circle A is (3, 7).
(a) Write the equation of the circle
(b) find the area of the circle.
(c) find the circumference of the circle
(d) what are the coordinates of the point that is the image of
(-2, 4) reflected through the center of the circle.
(e) write the equation of the tangent line to the circle through
the point (-2, 4)
notes 13.3
Find the distance between the parallel lines
y = -3x +9 and y = -3x + 5
April 26, 2017
notes 13.3
April 26, 2017
Suppose a triangle with vertices (0,0), (4,0) and (0, 3) is rotated
about the y-axis.
Describe the shape of the figure. Analyze the figure using your
knowledge base.
Revolve the triangle about the x-axis. Describe the shape and
analyze. What is true, not true about the different rotations.