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Tems11 [23]
3 years ago
12

Maggie graphed the image of a 90° counterclockwise rotation about vertex A of △ABC. Coordinates B and C of △ABC are (2, 6) and (

4, 3) and coordinates B’ and C’ of it’s image are (–2, 2) and (1, 4). What is the coordinate of vertex A?

Mathematics
1 answer:
Vitek1552 [10]3 years ago
8 0

Answer:

  A(2, 2)

Step-by-step explanation:

I find it useful to graph the given points. The center of rotation is at the place where the perpendicular bisectors of BB' and CC' meet. That point is ...

  A =  (2, 2).

__

The graph shows you the slope of BB' is 1, so its perpendicular bisector will have a slope of -1. The midpoint of BB' is (2-2, 6+2)/2 = (0, 4). This is the y-intercept of the line, so the perpendicular bisector of BB' has equation ...

  y = -x +4

The slope of CC' is -1/3, so its perpendicular will have a slope of -1/(-1/3) = 3. The midpoint of CC' is (4+1, 3+4)/2 = (5/2, 7/2). In point-slope form the equation of the perpendicular bisector of CC' is ...

  y -7/2 = 3(x -5/2)

  2y -7 = 3(2x -5) . . . . multiply by 2

  2(-x+4) -7 = 3(2x -5) . . . substitute for y

  -2x +1 = 6x -15 . . . . .eliminate parentheses

  16 = 8x . . . . . . . . . . add 2x+15

  x = 2 . . . . . . divide by 8

  y = -2+4 = 2 . . . . from the equation for y

The intersection of the perpendicular bisectors of BB' and CC' is the center of rotation:

  A = (2, 2)

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Simplify negative 5 minus the square root of negative 44 negative 5 minus 4 times the square root of 11 i negative 5 minus 4 i t
Anika [276]

Answer:

-5-\sqrt{-44}=-5-2\sqrt{11}i

Step-by-step explanation:

We want to simplify:

-5-\sqrt{-44}

We rewrite the expression under the radical sign to obtain:

-5-\sqrt{4\times11\times -1}

We split the expression under the radical sign to get:

-5-\sqrt{4} \times \sqrt{11} \times \sqrt{-1}

Recall that:

\sqrt{-1}=i

This implies that:

-5-\sqrt{4} \times \sqrt{11} \times \sqrt{-1}=-5-2\sqrt{11}i

Therefore -5-\sqrt{-44}=-5-2\sqrt{11}i

6 0
3 years ago
?<br> 5 in<br> Q 2 in R<br> PQ =
777dan777 [17]

Answer:

What is your specific question regarding Pq?

Step-by-step explanation:

4 0
2 years ago
Choose the equation for the situation "a fraction f multiplied by 13 equals 29". A. 1f⋅13=29 B. 3f=29 C. (f3⋅13)=29 D. 13f=29
Delicious77 [7]

Answer:

13f=29

Step-by-step explanation:

I hope this helps you out!

7 0
2 years ago
Help fast!! please.
alexira [117]

Answer:

Mean = 10

Variance = 30.89

Standard Deviation = 5.56

Step-by-step explanation:

Find the Mean, Variance and Standard deviation

6, 14, 8, 2, 11, 7, 12, 4, 18, 18

Step 1

We rearrange the data and find the Mean

2, 4, 6, 7, 8, 11, 12, 14, 18, 18

Mean = Sum of values/Number of values

= 2 + 4+ 6+ 7+ 8 + 11 + 12 + 14 + 18 +18/10

= 100/10

= 10

Step 2

We find the variance of this sample days ma

Variance = (x - Mean)²/n - 1

n = 10

Hence,

=( (2 - 10)² +(4 - 10)²+ (6 - 10)²+ (7 - 10)² + (8 - 10)² + (11 - 10)² + (12 - 10)² + (14 - 10)² + (18 - 10)² +(18 - 10)²) /10 -1

= ( 64 + 36 + 16 + 9 + 4 + 1 + 4 + 16 + 64 +64)/9

= 278/9

= 30.88888889

Approximately = 30.89

Step 3

Standard Deviation = √Variance

= √30.89

= 5.5578772926

Approximately = 5.56

6 0
3 years ago
4 2/3 divided by 1/2
ycow [4]

Answer:

9 1/3

Step-by-step explanation:

1. Make 4 2/3 into a improper fraction

4 2/3= 14/3

2. Keep, change, flip

14/3 x 2/1

3. Multiply

14/3 x 2/1= 28/3

4. Simplify

28/3= 9 1/3

(btw keep, change, flip basically means to keep the first fraction the way it is, change the division sign to a multiplication sign, then flip the second fraction so the original denominator is the new numerator, and vise versa.)

3 0
3 years ago
Read 2 more answers
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