Assume that T is a linear transformation. Find the standard matrix of T. T: set of real numbers R squaredℝ2 first reflects points through the line x 2 equals negative x 1line x2=−x1 and then reflects points through the line x 2 equals x 1line x2=x1.

Step-by-step explanation:

Thinking process:

We will need to test the different geometric transformations.

Let's see how this can be done:

Let the shear transformation be represented by the matrix S such that

Then, let the image be reflected by the reflection R, such that:

R = is reflected across the point

then the vector will be =

This is the mirror image.

Then it means that and

Thus, the standard matrix is given by:

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.