The point A (3, 4) is reflected over the line x = 2, and then is reflected over the line x = -4. What are the coordinates of A'? (9, 4)
(-9, 4)
(1, 4)
(1, 2)

9514 1404 393

  (-9, 4)

Step-by-step explanation:

Reflection over the line x=a performs the transformation ...

  (x, y) ⇒ (2a -x, y)

So, reflection over the two lines will give the transformation ...

  (x, y) ⇒ (2·2 -x, y) = (4 -x, y) . . . . . reflection over x=2

then ...

  (4 -x, y) ⇒ (2(-4)-(4-x), y) = (x -12, y) . . . followed by reflection over x=-4

__

Reflecting (3, 4) over the two lines gives an image point of ...

  (x, y) ⇒ (x -12, y)

  (3, 4) ⇒ (3 -12, 4) = (-9, 4)

The coordinates of A' are (-9, 4).

Comment on double reflection

Reflection over the two lines results in a translation that is double the distance between the two lines. The translation is in the direction that the second line is from the first. Here, the lines are 2 -(-4) = 6 units apart, with the second line being to the left of the first. The translation is 12 units to the left.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

x+14

step-by-step explanation: