Unit 6.7

2.  Formulas and the coordinate plane
 Distance formula
 To determine whether sides are congruent.
 To determine if diagonals are congruent.
 Midpoint formula
 To determine the coordinates of the midpoint of a side.
 To determine whether diagonals bisect each other.
 Slope formula
 To determine whether opposite sides are parallel.
 To determine whether diagonals are perpendicular.
 To determine whether sides are perpendicular.

3.  Is triangle ABC scalene, isosceles, or equilateral.

4. A(0,1), B(4,4), andC(7,0)
AB = (4 - 0)2 + (4 -1)2
= 16 + 9 = 25 = 5
BC = (7 - 4)2 + (0 - 4)2
= 9 +16
CA = (0 - 7)2 + (1- 0)2 = 49 +1
= 50 = 5 2
ABC is an
isosceles
triangle.

5.  Is parallelogram ABCD a rhombus? Explain.
slopeof AC = - =
5 0 5
4 ( 2) 6
- -
1 4 3
2 0 2
slopeof BD = - = -
-
Since the slopes are not opposite reciprocals,
the diagonals are not perpendicular.
Therefore, ABCD is not a rhombus.

6.  A kite is shown. What is the most precise
classification of the quadrilateral formed by
connecting the midpoints of the sides of the
kite?

7. A = æç - + + ö¸= - è ø
4 0 , 0 4 ( 2, 2)
2 2
B = æç + + ö¸= è ø
0 8 , 4 0 (4,2)
2 2
C = æç + + - ö¸= - è ø
8 0 , 0 ( 4) (4, 2)
2 2
D = æç + - - + ö¸ = - - è ø
0 ( 4) , 4 0 ( 2, 2)
2 2
AB =| 4 - (-2) |= 6
BC =| -2 - 2 |= 4
CD =| -2 - 4 |= 6
DA =| 2 - (-2) |= 4
Opposite sides are congruent. Sides are vertical and
horizontal, making them perpendicular. Therefore,
ABCD is a rectangle.

8. PPRRAACCTTIICCEE

11. AANNSSWWEERRSS

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