Geometry Unit 8: Coordinate Geometry Geometry

GeometryUnit8:CoordinateGeometry

Ms.Talhami 1


Name_________________


Ms.Talhami 2

HelpfulVocabularyWord Definition/Explanation Examples/HelpfulTips


Ms.Talhami 3

In the given triangles below, find the values for x. Find the distance between the two endpoints of each line segment:

12

16

x x

8

15


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Now find the distance between the two endpoints of the line segment below:

DistanceFormula


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Practice Find the distance between the two endpoints of each line segment:

Find the distance between each set of points:

(-3, 2) and (-9, -6)

(2, -3) and (6, 0) (1, 2) and (-11, 7)

(2, 2) and (6, 5)

(-3, 0) and (3, 8) (0, 1) and (-4, -2)

(-2, 1) and (-5, 5)

(0, 0) and (-5, 12) (0, 1) and (3, 5)

Take it a Step Further

Show that the triangle with the following vertices is isosceles: 1,0 , 5,0 , %&'(3,4)


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Midpoint

Identify the number that is exactly in the middle of each pair of numbers:

2 10

-16 -4

-7 7 Find the midpoint of the following line segments:


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Now find the midpoint of the following line segment:

MidpointFormula


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Practice Find the midpoint of the following line segments:

Find the midpoint for each set of points:

(-3, 2) and (-9, -6)

(2, -2) and (6, 0) (1, 2) and (-11, 8)

(2, 1) and (6, 5)

(-3, 0) and (3, 8) (0, 1) and (-4, -3)

(-2, 1) and (-6, 5)

(0, 0) and (-4, 12) (-1, 1) and (3, 5)


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Slope In your own words, write down a definition for slope. Identify the types of slopes:

Practice Finding Slope 1) (8, 10), (−7, 14) 2) (−3, 1), (−17, 2) 3) (−20, −10), (−12, −4) 4) (−12, −5), (0, −8) 5) (−19, −6), (15, 16) 6) (−6, 9), (7, −9) 7) (−18, −20), (−18, −15) 8) (11, −18), (12, 12) 9) A line segment has endpoints (1, 5) and (3, k), and a slope of 4. Find the value of k, and the midpoint of the line segment.


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Parallel and Perpendicular Slopes Parallel Slopes Perpendicular Slopes

Determine if the points passing through line L1 and line L2 are parallel, perpendicular, or neither.

f. Is it possible for two lines with negative slopes to be perpendicular? Explain why or why not.


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Equations of Lines

Do Now: Find the slope of a line that passes through the points (-3, -4) and (5, 4). What do we know about the equation of a line?

Write the equation of the lines below:


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Find the equation for each line with the given information: a. Passes through: (1, 0) Slope: 2

b. Passes through: (2, 1) Slope: 3/4

c. Passes through: (-3, 4) Slope: -1/2

d. Passes through: (-4, -1) Y-intercept: 5

e. Passes through: (8, 6) Y-intercept: -2

f. Passes through: (-6, 4) Y-intercept: 0

g. Passes through: (3, 3)and (-3, 7)

h. Passes through: (8, 5) and (1, 3) i. Passes through: (4, a) and (-5, a)

1) Find the equation of the line that passes through the point (5, -4) and has a slope of -2. 2) Find the equation of the line that passes through the point (4, 3) and has a y-intercept of -3. 3) Find the equation of the line that passes through the points (-2, 5) and (6, -1). 4) If the point (5,k) lies on the line represented by the equation - = −21 + 9, what is the value of k?


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Write the equations for the line segments of the function on the graph below for the given domains: (a) -7<x<-4(b) -4<x<0 (c) 0<x<2(d) 2<x<6 (e) 6<x<7

Parallel and Perpendicular Lines

1) Write the equation of the line -1 that passes through the points (-4, 5) and (2, -4). 2) Write a second equation for the line -2 that passes through the points (-5, 0) and (4, 6). 3) Write a third equation for the line -3 that passes through the points (-3, -1) and (1, -7). 4) Graph and label all three equations on the set of axes: What do you notice about the slopes of equations -1 and -2? What do you notice about the slopes of equations -1 and -3?


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Practice

1) Find the slope of a line parallel to a line with the given slopes:

23 -3 5 −12

2) Find the slope of a line perpendicular to a line with the given slopes:

23 -3 5 −12

3) Identify whether the following equations are parallel, perpendicular, or neither:

- = 21 + 6- = 41– 1

31 + 4- = 961 + 8- = 4

21– 5- = 10101– 4- = 16

41– 2- = 661 + 3- = 8

4) Write the equation of a line parallel to - = 7

8 1– 1 that passes through the point (-2, 3). 5) Write the equation of a line perpendicular to - = − 8

9 1– 3 that passes through the point (3, 4).


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6) A line perpendicular to - = 78 1 + 3 passes through the point (1, -4). At which point do these two lines

intersect? Draw both lines on the graph below and label their point of intersection:


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Perpendicular Bisectors

Find the midpoint of the line segment with endpoints (-5, -4) and (7, 6). Find the equation for this line segment on the given interval. Create an equation for a new line that also passes through this midpoint. Graph the line segment, midpoint, and your new line on the set of axes. What do we know about perpendicular bisectors?

How can we find the perpendicular bisector for the line segment with endpoints (-1, 4) and (3, -2)?


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Practice 1) Find the equation of the perpendicular bisector of the line segment joining the points (-3, 5) and (3, -1). 2) The line - = − :

; 1 + 2 is the perpendicular bisector of a line segment that has an endpoint of (5, 6). Find the other endpoint. 3) Given two line segments, one joining points (-5, 0) and (1, 6) and the other joining points (2, 4) and (6, -2), find the coordinate where their perpendicular bisectors intersect. Then, draw the segments and their perpendicular bisectors on the graph below:

Geometry Unit 8: Coordinate Geometry Geometry

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