Preparing for the Regents Examination Geometry, AK

20 Use constructing congruent angles procedure.
21 Use angle bisector procedure on each side of
the triangle. The angle bisectors should meet
at a common point, P.
22 Use constructing a perpendicular bisector
procedure.
Transformations and
the Coordinate Plane
6-1 Cartesian Coordinate
System
(pages 91–92)
1 (2) 5
2 (2) 6
3 (4) 10
4 (2) 6
5 (1) √ 2
6 (2) √ 226
7 a A(5, 2), B(3, 3) b A(3, 4), B(0, 5)
c A(x, y), B(0, 0)
8 The length of base ___
AB is the difference
between the x-coordinates of A and B;
6 2 4. The height is the vertical distance
from C to ___
AB or the difference between the
y-coordinates; 4 1 3. Therefore,
A 1 _ bh
2 1 _ (4)(3) 6.
2
9 The length of the base ___
AB is the difference
between the x-coordinates of A and B;
1 (3) 4. The height is the vertical distance
from C to ___
AB or the difference between
the y-coordinates; 8 4 4. Therefore,
A 1 _ bh
2 1 _ (4)(4) 8.
2
28 Chapter 6: Transformations and the Coordinate Plane
23 Copy one side and the angles at each vertex.
Extend the rays until they meet.
24 Use the line bisector procedure. Mark the
intersection of the line and its bisector as the
midpoint.
CHAPTER
6
10 The length of the base −−
AB is the difference in
the y-coordinates of A and B; 6 2 4. The
height is the horizontal distance from C
to −−
AB or the difference between the
x-coordinates; 3 2 1. Therefore,
A 1 _ bh
2 1 _ (4)(1) 2.
2
11 The length of the base ___
AB is the difference
between the y-coordinates of A and B;
8 2 6. The height is the horizontal distance
from C to ___
AB or the difference between
the x-coordinates; 4 (2) 6. Therefore,
A 1 _ bh
2 1 _ (6)(6) 18.
2
12 D(x, y) (1, 2)
13 Draw a horizontal line from A to C. For
ABC, the length of the base ___
AC is the difference
between the x-coordinates of A and C;
3 (7) 10. The height is the vertical distance
from B to ___
AC or the difference between
the y-coordinates; 5 1 4. The area of
ABC is A 1 _ bh
2 1 _ (10)(4) 20. For
2
ADC, the base is 10 and the height is 4. The
area of ADC is A 1 _ bh
2 1 _ (10)(4) 20.
2
The area of quadrilateral ABCD is 20 20
40.