MidPoint Formula Guided Practice 1.
2.
at (-2, 0), with 1 unit equaling 1 block. If Megan could take a bird’s straight flight path from one site to the other, what would the distance be? A 1.41 blocks C 2.24 blocks B 1.73 blocks D 2.42 blocks
( 5, 2)
3.
4 The diameter of a circle is shown below.
(6, 5.5)
( 8, 4)
Daylily
Iris
Chrysanthemum (1, 2) Daylily
What is the length of the circle’s diameter? F 6.71 units H 10.82 units G 8.24 units J 12.37 units
(2.5, 5)
Justin plans to place a small fountain at the center of the garden. What would be its coordinates? F (1.5, 5.75) H (4.25, 3) G (1.75, 2.5) J (8.5, 6) 54
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The arbor will be built at the midpoint of the sidewalk’s length. Which coordinate pair marks the midpoint? A (0.5, 2.5) C (1, 1) B (0.5, 0.5) D (5.5, 2.5)
2 After seeing the Four Seasons Garden at Fort Worth, Justin decides that a four seasons garden would make a perfect wedding present for his older sister. He plans the garden as shown, with the coordinates (6,5.5) and (2.5,5) marking a line that forms the diameter of the garden.
Mastering the TAKS, Grade 11
011-075_OB_TX_877327.indd 54
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ed to derive and use formulas involving length, slope, and
y walks xicano to . If the two lane, the the palace g 1 block. raight flight what would
locks locks
Garden hat a four perfect sister. with the marking a the garden.
6, 5.5)
mum
untain at would be its
3) )
3 Padma wants to build an arbor across a sidewalk that angles from her house to the street. When she lays out the plot plan for the house and grounds, the endpoints of the sidewalk are located at (-5, -2) and (6, 3), as shown. (6, 3)
( 5, 2)
The arbor will be built at the midpoint of the sidewalk’s length. Which coordinate pair marks the midpoint? A (0.5, 2.5) C (1, 1) B (0.5, 0.5) D (5.5, 2.5) 4 The diameter of a circle is shown below.
( 8, 4) (1, 2) What is the length of the circle’s diameter? F 6.71 units H 10.82 units G 8.24 units J 12.37 units
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ose the
4.
6/28/06 3:53:38 PM
Assignment #2 1.
2.
X =
( 4.5, 6 )
Y = ( 12.5, 0 )
( x1, y1 ) TAKS Review Step
( x2 , y 2 ) Lesson 19
2: Use the distance formula to find XY.
Example 3.
d =
( x2 − x1 )2 + ( y 2 − y1 )2
ΔABC has vertices at A(0, 0) , B(9, 12) , and C(25, 0) . What is the distance between
d =
(12.5 − 4.5)2 + (0 − 6)2
d =
(8)2 + ( −6)2
d =
64 + 36
the midpoint of AB and the midpoint of AC ?
A
7.5 units
B
10 units
C
15 units
D
20 units
Solution d = 100 = 10 If you notice, the coordinates given do not make graphing very easy to do. The answer is choice B. Instead, we will sketch the relative position of the given points, so that we can 4. better visualize the problem. Example y B (9, 12)
A coordinate grid is placed over a map.
9
City A is located at ( −4, 3) and city B is Sketch the triangle. located at (3, 9) . If City C is at the
7 6 5 3
C (25, 0)
2
which is closest to the distance in
1 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2
coordinate units from City A to City C?
A
8
4
midpoint between City A and City B, A(0, 0)
−1 −2
4.61 units
−3
B (9, 12)
B
6.52 units
C
9.22 units
D
21.25 units
X
A(0, 0)
C (25, 0) Y
10
Next, sketch in the −4 −5 midpoint of AB and the −6 7 midpoint of AC . We−will −8 call them X and Y. −9 Connect them. This is the distance we wish to find.
Now we will solve the problem using formulas.
9
3 4
5 6
7 8
9
x