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
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.
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).
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
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
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?
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?
Reflect the line y= -1/2x +3 over the y-axis
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
Find the equation of the tangent line to the circle with equation x^2-8x +y^2 +8y=201 at the point (9, 8)
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.
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
An interesting application of systems... Find the distance between the parallel lines y= 3x + 5 y = 3x -2 and
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
notes pd5 13.4 April 26, 2016 Graph y < -2x -5 and y > 3/2x -7 Graph y < x-4
notes pd5 13.4 April 26, 2016
notes pd5 13.4 April 26, 2016 Graph the solution set for y < x^2 +2 and y > -1 graph x^2 + y^2 < 36 y> x-1
Work in small groups and investigate #9 on page 625 of your book. This is a beginners look at calculus!
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.
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
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)
(8, 2) (10, 0) Find the area and circumference of the circle
13.7 Coordinate Geometry Practice What is the area of the shaded region (-6,2) (2,2) (-6,-4) (2,-4)
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)
Find the distance between the parallel lines y = -3x +9 and y = -3x + 5
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.