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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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Step-by-step explanation:

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Answer:

There are 364 ways of filling the offices.

Step-by-step explanation:

In this case, the order of filling of the offices does not matter, so, we can figure out the different ways of filling the offices by using the combination formula:

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where n=14 (number of members)

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n!=n·(n-1)·(n-2)·...·3·2·1

C^{14} _{3}=\frac{14!}{(14-3)!3!}=\frac{14*13*12*11*10*9*8*7*6*5*4*3*2*1}{(11*10*9*8*7*6*5*4*3*2*1)*(3*2*1)}=\frac{14*13*12}{3*2*1} =364

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3 years ago
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Step-by-step explanation:

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1. Four times a number minus twenty-one is the same as six times
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Answer: -16

Step-by-step explanation:

Let the number be y

Four times a number minus twenty-one can be written as:

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The number is -16

7 0
3 years ago
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