GEOMETRY HONORS COORDINATE GEOMETRY PACKET

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Chester Daniels
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1 GEOMETRY HONORS COORDINATE GEOMETRY PACKET Name Period

2 Homework Lesson Assignment Day 1 - Slopes of Perpendicular WKSHT and Parallel Lines Day 2 - Writing an Equation of a Line HW- Honors TXTBK pages # 1c, 2d, 3, 4, 6 a-e, 8 a- g, 9, 10, 22 Answers : 1c; ½ and - 3, 2d; y = ½x + ¼ slope: ½ and y- intercept: ¼ 3; y = -6 4; x = 8 6a. y = 4x +2 b. y = 5x -2 c. y = 10x + 1 d. y = -2x 5 e. y = -x + 2 8a. y -1 = 3(x-2) b. y-3 = -1/2(x + 6) c. y 5 = 0 d. y = 7 (x -2) e. y = -4(x-3) f. x = -3 g. y 7 = 3/2 (x -8) 9; ¾ 10; y = 3/2 x + 5/2 22; y = x 3 2 and y = -x Day 3 - Writing Equations of Altitudes, Medians and Perpendicular Bisectors HW- Honors TXTBK page 616 # 13 19, 24 Answers: 13. y -12 = 1/7 (x -4) 14. y = -7x y = -7x y = -2x /7 18. a. y = 2 b. x = y 7 = -1/2 (x + 1) 24. equations of medians: x =2, y =x and y = -x + 4. They intersect at (2,2). Day 4 - Solving Systems of Equations HW- Honors TXTBK page 620 #1, 2, 4, 5, 6 Answers: 1a. (6,4) 1b. (2,5) 1c. (-3, -7) 1d. (3, 2) 2a. (4, 3) and (4, -3) 2b. (1, 3) 4a. 4b. (4, 17) 5. (-2, -3) 6. (a, 6-1.5a) Day 5 - Writing Equations of a Line Using Points of Intersection HW- Honors TXTBK pages # s 7, 9, 10, 12, 14, 15 Answers: 7. (4,-2) 9. y-1 = 5(x-2) or y = 5x y = -2/3x = 3 1/3 12. (-8, -23)

3 Day 1 - Slopes of Perpendicular and Parallel Lines 1. a) Graph AB with coordinates A(-2,-5) and B(6,-1). b) Graph CD with coordinates C(-1,3) and D(2,-3). c) Find the slope of AB and CD. d) Are the lines parallel or perpendicular? 2. a) Graph AB with coordinates A(-1,4) and B(2,6). b) Graph CD with coordinates C(1,0) and D(4,2). c) Find the slope of AB and CD. d) Are the lines parallel or perpendicular?

4 3. a) Graph AB with coordinates A(2,3) and B(4,-1). b) Graph CD with coordinates C(-3,-5) and D(1,1). c) Find the slope of AB and CD. d) Are the lines parallel or perpendicular? Do you notice a relationship between the slopes of parallel lines and perpendicular lines? Practice 1. If the line joining S(2,3) and P(7,9) is perpendicular to the line joining Q(8,k) and R(2,4), find the value of k. 2. The slope of AB is 4/7 and the slope of CD is 7/k. If AB CD, what is the value of k? 3. If the line joining A(3,5) and B(1,2) is parallel to the line joining R(7,k) and G(5,6), what is the value of k?

5 The equation of a line in slope intercept form is y = mx + b, where m is the slope and b is the y intercept. The standard form of an equation is ax + by = c. To find the slope, we use the formula: slope = Identifying Slopes of Parallel and Perpendicular Lines 1. What is the slope of a line parallel to the line y 4x 5? 2. What is the slope of a line parallel to the line whose equation is 2y 3x 7? 3. What is the slope of a line parallel to the line whose equation is 2x 3y 12? 4. What is the slope of a line perpendicular to the line whose equation is y = 2x 5? 5. What is the slope of a line perpendicular to the line whose equation is 6y 2x 6? 6. What is the slope of a line perpendicular to the line whose equation is 3x y 8 0?

6 Day 2 - Writing an Equation of a Line Method 1 Slope intercept form: Method 2 Point Slope Form: y = mx +b y y 1 = m ( x x 1 ) Examples: 1. Write an equation of a line that is parallel to the line 2x + y =6 and whose y-intercept is the same as the line y = x Write an equation of a line perpendicular to y = 3 1 x -6 and has a y-intercept of zero. 3. Write an equation of a line that passes through the point (2,3) and has a slope of Write an equation of a line that passes through the point (1,5) and is perpendicular to 2y = x -6.

7 5. Write an equation of a line that passes through the points (-1,-2) and (5,1). 6. Find an equation of a line with a slope of 3 and an x intercept of Write an equation of a line that is parallel to the y axis and contains the point ( 6, 1).

8 Day 3 - Writing Equations of Altitudes, Medians and Perpendicular Bisectors A median of a triangle is a line segment drawn from the vertex of a triangle to the midpoint of the opposite side. How to calculate the median to side of ABC An altitude of a triangle is a line segment drawn from a vertex of a triangle perpendicular to the opposite side. How to calculate the altitude to side of ABC A perpendicular bisector of a line segment is a line (or line segment) that is perpendicular to the segment at its midpoint. How to calculate the bisector to side of ABC

9 1. In triangle ABC, A (-3,2), B(8,4) and C(5,10). a. Find an equation of the median to AB. b. Find an equation of the perpendicular bisector of AB. c. Find an equation of the altitude to AB.

10 2. Given ABC, A(-3,2), B(6,5) and C(-2,9): a. Find an equation of the median to AB. b. Find an equation of the perpendicular bisector of AB. c. Find an equation of the altitude to AB.

Day 4 - Solving Systems of Equations When two lines are graphed in the same coordinate plane on the same set of axes, only one of the following three possibilities can occur.

Dependent the lines coincide, that is, they are the same line with an infinite number of ordered pairs in common. Case 1 Case 2 Case 3 To solve a system graphically: 1.

11 Day 4 - Solving Systems of Equations When two lines are graphed in the same coordinate plane on the same set of axes, only one of the following three possibilities can occur. The pair of lines will be: 1. Consistent intersect in only one point and have one ordered number pair in common. 2. Inconsistent the lines are parallel and have no ordered number pairs in common. 3. Dependent the lines coincide, that is, they are the same line with an infinite number of ordered pairs in common. Case 1 Case 2 Case 3 To solve a system graphically: 1. Graph each line on the same set of axes 2. Find the common solution To solve a system algebraically using elimination: 1. Transform each equation into equivalent equations in which the variables appear on one side and the constant appears on the other. 2. Eliminate a variable by manipulating the equations to produce additive inverses. 3. Add the two equations and solve for the remaining variable. 4. Substitute the variable you found into either original equation and solve for the remaining variable. To solve a system algebraically using substitution: 1. Transform one of the equations into an equivalent equation in which one of the variables is expressed in terms of the other. 2. Substitute the expression you found in the other equation. Your equation should only contain one variable. 3. Solve for the variable. 4. Substitute the variable you found into either original equation and solve for the remaining variable.

12 Examples 1. Solve the system of equations graphically: x + y = 2 2x y = 1 2. Solve the system algebraically using elimination: 7x = 5 2y 3y = 16 2x 3. Solve the system algebraically using substitution: 3x 4y = 26 x + 2y = 2

13 4. Solve the system: 3x = 4y 3x 8 3y The owner of a men s clothing store bought six belts and eight hats for $140. A week later, at the same prices, he bought nine belts and six hats for $132. Find the price of a belt and the price of a hat. 6. Mr. Black bought 2 pounds of veal and 3 pounds of pork, for which she paid $ Mr. Cook, paying the same prices, paid $11.25 for 1 pound of veal and 2 pounds of pork. Find the price of a pound of veal and the price of a pound of pork.

14 Day 5 - Writing Equations of a Line Using Points of Intersection 1. Write the equation of a line that contains the point of intersection of the graphs x = 4 and y = 2x + 8 and is parallel to the line whose equation is y = -2x Write the equation of a line that contains the point of intersection of the graphs 1 8x 3y = 7 and 10x + 4y = -1 and is perpendicular to the line y x 7. 3

15 Using Equations of Lines to Find the Coordinates of an Altitude. 1. In ABC with coordinates A(-3,4), B(6,-2) and C(7,6) altitude is drawn. Find the coordinates of D. 2. In ABC with coordinates A(0,0), B(6,3) and C(1,5) altitude is drawn. Find the coordinates of D.

GEOMETRY HONORS COORDINATE GEOMETRY PACKET

GEOMETRY HONORS COORDINATE GEOMETRY PACKET Name Period 1 Day 1 - Directed Line Segments DO NOW Distance formula 1 2 1 2 2 2 D x x y y Midpoint formula x x, y y 2 2 M 1 2 1 2 Slope formula y y m x x 2 1