MidPoint  Formula  Guided  Practice    1.  

         

2.  

               

3.  

                           

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54 Mastering the TAKS, Grade 11

Read each question and choose the best answer.

1 In San Antonio, Megan’s family walks from the Instituto Cultural Mexicano to the Spanish Governor’s Palace. If the two were plotted on a coordinate plane, the Instituto might be at (0, 1) and the palace at (-2, 0), with 1 unit equaling 1 block. If Megan could take a bird’s straight fl ight path from one site to the other, what would the distance be? A 1.41 blocks C 2.24 blocksB 1.73 blocks D 2.42 blocks

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.

Chrysanthemum

Daylily

Iris

Daylily

(2.5, 5)

(6, 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)

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 unitsG 8.24 units J 12.37 units

G.7(C) The student is expected to derive and use formulas involving length, slope, and midpoint.

TAKS PracticeOBJECTIVE 7

011-075_OB_TX_877327.indd 54011-075_OB_TX_877327.indd 54 6/28/06 3:53:38 PM6/28/06 3:53:38 PM

4.    

                               

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54 Mastering the TAKS, Grade 11

Read each question and choose the best answer.

1 In San Antonio, Megan’s family walks from the Instituto Cultural Mexicano to the Spanish Governor’s Palace. If the two were plotted on a coordinate plane, the Instituto might be at (0, 1) and the palace at (-2, 0), with 1 unit equaling 1 block. If Megan could take a bird’s straight fl ight path from one site to the other, what would the distance be? A 1.41 blocks C 2.24 blocksB 1.73 blocks D 2.42 blocks

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.

Chrysanthemum

Daylily

Iris

Daylily

(2.5, 5)

(6, 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)

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 unitsG 8.24 units J 12.37 units

G.7(C) The student is expected to derive and use formulas involving length, slope, and midpoint.

TAKS PracticeOBJECTIVE 7

011-075_OB_TX_877327.indd 54011-075_OB_TX_877327.indd 54 6/28/06 3:53:38 PM6/28/06 3:53:38 PM

Assignment  #2      1.    

 2.    

             

3.    

     4.      

 

TAKS Review Lesson 19

9

Example ABCΔ has vertices at (0, 0)A , (9, 12)B , and (25, 0)C . What is the distance between

the midpoint of AB and the midpoint of AC ? A 7.5 units B 10 units C 15 units D 20 units Solution

If you notice, the coordinates given do not make graphing very easy to do. Instead, we will sketch the relative position of the given points, so that we can better visualize the problem.

Now we will solve the problem using formulas.

(0, 0)A

(9, 12)B

(25, 0)C

Sketch the triangle.

(0, 0)A

(9, 12)B

(25, 0)C

Next, sketch in the midpoint of AB and the midpoint of AC . We will call them X and Y. Connect them. This is the distance we wish to find.

X

Y

TAKS Review

10

Step 1: Find the coordinates of X and Y using the midpoint formula.

( )

1 2 1 2,2 2

0 9 0 12,2 2

4.5, 6

x x y yM

X

X

+ + =

+ + =

=

( )

1 2 1 2,2 2

0 25 0 0,2 2

12.5, 0

x x y yM

Y

Y

+ + =

+ + =

=

Step 2: Use the distance formula to find XY.

2 22 1 2 1

2 2

2 2

( ) ( )

(12.5 4.5) (0 6)

(8) ( 6)

64 36

100 10

d x x y y

d

d

d

d

= − + −

= − + −

= + −

= +

= =

The answer is choice B. Example A coordinate grid is placed over a map. City A is located at ( 4, 3)− and city B is

located at (3, 9) . If City C is at the

midpoint between City A and City B, which is closest to the distance in coordinate units from City A to City C? A 4.61 units B 6.52 units C 9.22 units D 21.25 units

12345

54321

6

6

6−

6−

7

7

7−

7−

8

8

8−

8−

9

9

9−

9− 5− 4− 3− 2− 1− 0

5−4−3−2−1−

x

y

1 1( , )x y 2 2( , )x y