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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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Answer:
3 times

Explanation:
We know that:
small diameter = 2 * 10^-2 in
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We want to know how many times larger is the thin diameter compared to the large one.
We will do this as follows:
large diameter = k * small diameter
where k is the number of times that we want to find
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This means that the large diameter is 3 times the small one.

Hope this helps :)
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3 years ago
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sweet-ann [11.9K]

Answer:

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Step-by-step explanation:

Hope this was helpful let me know if it was!

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Subtract 124 and 18
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2 years ago
The equation of a circle is given below. (x-0.5)^{2}+(y-3.5)^{2} = 16(x−0.5) 2 +(y−3.5) 2 =16left parenthesis, x, minus, 0, poin
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Answer:

<h2>The radius is 4 units long.</h2>

Step-by-step explanation:

The given equation is

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