CC Geometry H
Aim #2: How do we write inequalities that describe a region on the coordinate plane?
Do Now:
1. State the inequality that divides the plane in half in each example.
c)
b)
d)
a)
y
y
y
y
2
x
2
x
x
­1
x
­3
2. Graph the inequalities:
a) y < 2x + 1
b) y ≥ -3x - 1
Exercises: Graph each system of inequalities.
Shade the intersection of the two half-planes.
1.
y≥1
x≤5
a) Is (1,2) a solution? Explain.
b) Is (1,1) a solution? Explain.
c) The region is the intersection of
how many half-planes? Explain.
2.
a) Is (-2,4) in the solution set?
y < 2x + 1
y ≥ -3x - 2
b) Is (1,3) in the solution set?
c) The region is the intersection of
how many half-planes? Explain.
We will now try to describe a given region based on x and y coordinates used.
(15,7)
(1,2)
1. Name three points inside the rectangular region.
2. Name three points on the boundary of the rectangular region.
3. What are possible values of x used in the region and on the boundary?
4. What are possible values of y used in the region and on the boundary?
5. What is the length of a diagonal of the rectangular region?
6. Name a point within the rectangular region and on the diagonal that connects
(1,2) and (15,7).
Exercises
1. Given the region to the right:
a) Name three points in the region.
b) Name three points on the boundary.
c) Write two inequalities that describe the x-values
in the region.
d) Write two inequalities that describe the y-values
in the region.
e) Write (c) and (d) as a system of two compound inequalities:
{ (x,y) |
f) Will the lines x = 4 and y = 1 pass through the region? Draw them.
2. The region shown continues unbound to the right.
a) Name three points in the region.
b) Describe in words the points in the region,
using boundary lines in your response.
c) Write the system of inequalities that
describes the region.
d) Name a horizontal line that passes through the region.
3. Given the region that continues downward without bound as shown:
a) Describe the region in words.
b) Write the system of inequalities that describe
the region.
c) Name a vertical line that passes through
the region.
4a) Draw the triangular region in the plane given by
the triangle with vertices A(0,0), B(1,3) and C(2,1).
b) Write a set of inequalities that describes the
region.
5. Given the triangular region shown, describe
this region with a system of inequalities.
6. Given the trapezoid with vertices (-2,0), (-1,4), (1,4), and (2,0), describe
this region with a system of inequalities.
4
3
2
1
-2
-1.5
-1
0
0
-0.5
0.5
1
1.5
2
-1
Let's Sum it Up!
To write a system of inequalities for a triangular region in the plane,
• Identify the endpoints of each segment and find the slope.
• Write the equation of the line containing each segment.
• Identify the segment of the line by restricting the domain.
• Make the equations into inequalities that include points inside the region.
The general equation of a vertical line segment is x = c where c is a constant.
Then y-values would have to be restricted.
Name ______________________
Date ______________________
CC Geometry H
HW #2
1. Given the region shown:
a) Name three points in the region.
b) Identify the coordinates of the four vertices.
c) Write the system of inequalities describing this region.
2. Given the region shown:
a) How many half-planes intersect to form this
region?
b) Name three points on the boundary of the
region.
c) Describe the region in words.
d) Write the system of inequalities that describes the region.
3. Region T is shown to the right.
a) Write the coordinates of the vertices.
b) Write a system of inequalities that describes
this region.
c) What is the length of the diagonals to nearest tenth?
d) Give the coordinates of a point that is both in the region and on one of the
diagonals.
4. Given the trapezoidal region show to the right
a) Write the system of inequalities describing the
region.
b) Translate the region to the right 3 units
and down 2 units.
c) Write the system of inequalities describing
the translated region.
Mixed Review:
1) Using a compass and straightedge, construct the angle bisector of ≮CDE.
2) In right triangle FGH, m≮GHF = 90, altitude HJ is drawn to FG. Find the length
of JG and HJ algebraically.