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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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At 6:00 PM, a flagpole that is 35 feet tall casts a shadow that is 50 feet long. At the same time, how long will a person's shad
sertanlavr [38]

<u>Answer:</u>

The length of the person’s shadow is 5.7ft

<u>Explanation:</u>

Length of the flagpole =a= 35ft

Length of the shadow of the flagpole= b=50ft

Length of the person=c= 4ft

Suppose the length of the person’s shadow is=d

According to the  rules of trigonometry

\frac{\text { Length of the flagpole }}{\text { Length of the shadow of the flagpole }}=\frac{\text { Length of the person }}{\text { Length of the person's shadow }}

\frac{a}{b}=\frac{c}{d}

\frac{35}{50}=\frac{4}{d}

35d=200

d=\frac{200}{35}

d=5.7ft  

Hence, The length of the person’s shadow is 5.7ft.

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Step-by-step explanation:

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