Name ________________________________________________
Geometry R Unit 12 Review
Date: _________________
Period ______
1. Given the triangular region shown with vertices 𝑨(−𝟐, −𝟏), 𝑩(𝟒, 𝟓),
and 𝑪(𝟓, −𝟏):
a. Describe the systems of inequalities that describe the region
enclosed by the triangle.
𝑩
𝑨
𝑪
b. Rotate the region 𝟗𝟎° counterclockwise about Point 𝑨. How will
this change the coordinates of the vertices?
c.
Write the system of inequalities that describe the region enclosed in the rotated
triangle.
2. Consider the rectangular region:
1
a. Does a line with slope 2 passing through the origin intersect
(𝟒, 𝟒)
this region? If so, what are the boundary points it intersects?
What is the length of the segment within the region?
(𝟏, 𝟏)
b. Does a line with slope 3 passing through the origin intersect this region? If so, what are the
boundary points it intersects?
3. Consider the triangular region in the plane given by the triangle (−𝟏, 𝟑), (𝟏, −𝟐), and
(−𝟑, −𝟑).
a. The horizontal line 𝑦 = 1 intersects this region. What
are the coordinates of the two boundary points it
intersects? What is the length of the horizontal
segment within the region along this line?
b. What is the length of the section of the line
2𝑥 + 3𝑦 = −4 that lies within this region?
c. If the robot starts at (1, −2) and moves horizontally left at a constant speed of 0.6 units per
second, when will it hit the left boundary of the triangular region?
4. Find the area of the triangles with vertices O(0,0), A(5,-3), and B(-2,6), first by finding the
area of the rectangle enclosing the triangle and subtracting the area of the surrounding
𝟏
triangles, then by using the formula |𝟐 (𝒙𝟏 𝒚𝟐 − 𝒙𝟐 𝒚𝟏 )|.
5. Find the area of the triangle given using both the “boxing in” method and the General
formula for the area of a triangle.
6. Find the perimeter and the area of the quadrilateral with vertices 𝐴(−3, 4), 𝐵(4, 6), 𝐶(2, −3), and
𝐷(−4, −4) using the “boxing in” method.
7. Find the area of the pentagon with vertices 𝑨(𝟓, 𝟖), 𝑩(𝟒, −𝟑), 𝑪(−𝟏, −𝟐), 𝑫(−𝟐, 𝟒), and 𝑬(𝟐, 𝟔)
using the General Formula for area of a triangle.
8. Graph the following:
1
a. 𝑦 < 2 𝑥 − 4
2
b. 𝑦 ≥ − 3 𝑥 + 5
For Problems 9 & 10 below, a triangular or quadrilateral region is defined by the system of
inequalities listed.
a.
b.
c.
d.
9.
Sketch the region.
Determine the coordinates of the vertices.
Find the perimeter of the region rounded to the nearest hundredth, if necessary.
Find the area of the region rounded to the nearest tenth, if necessary.
𝑥≤6
1
𝑦 ≤ 3𝑥 + 2
𝑦 ≥ −𝑥 − 2
1
𝑦 ≥ 2𝑥 − 5
10.
𝑦 ≥ −2𝑥 − 2
1
𝑦 ≤ −4𝑥 + 5
𝑦 ≤ −𝑥 + 8
𝑦 ≥ −4
11. If the center of dilation is NOT on the line, then the dilation will produce a ____________________
line with the same __________________ .
12. If the center of dilation is NOT on the line, how do you find the y intercept?
2
13. The line y   x  2 is graphed below. Write the equation of the image of this line after a
3
dilation of 4 centered at the origin. (HINT: Is the center of dilation on the line?)
14. The equation of line is
. . What is the equation of the new line after a dilation of scale
factor 4 with center at the origin? (HINT: SOLVE FOR Y FIRST)
1)
2)
3)
4)
15. The equation of line is 2x + y = 1. What is the equation of the line after a dilation of scale factor
4 with center (1, -1)? (HINT: SOLVE FOR Y FIRST, is 1,-1 on line?)
16. Which of the following linear functions would remain unchanged under a dilation of 2 about
the origin?
(1) y = -5x
(2) y = 2x – 2
(3) y = ½ x + 2
(4) y = x + 1