Given that line segments are taken to line segments of the same length during rigid transformations, which transformation maps the line segment ab onto itself? a) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → x-axis reflection b) rotation counterclockwise of 90° → y-axis reflection → rotation counterclockwise of 270° → y-axis reflection c) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection d) rotation counterclockwise of 180° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection

B) rotation counterclockwise of 90° → y-axis reflection → rotation counterclockwise of 270° → y-axis reflection

Rotate the line counterclockwise 90 degrees so that it's now facing top left and bottom right and the slope is negative going down. Now reflect it to the left over the y-axis which is the straight up vertical line. Then, reflect it back to the right and rotate it 270 degrees putting it back at the beginning so now it equals 360 degrees which is a full circle.

Step-by-step explanation:

rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection

Rotation counterclockwise of 90° (x, y) → (−y,  x )

A(1, −2) → (2, 1)

B(4, 3) → (−3, 4)

x-axis Reflection (x, y) → (x, −y)

A(2, 1) → (2, −1)

B(−3, 4) → (−3, −4)

Rotation counterclockwise of 270° (x, y) → (y, −x )

A(2, −1) → (−1, −2)

B(−3, −4) → (−4, 3)

y-axis Reflection (x, y) → (−x, y)

A(−1, −2) → (1, −2)

B(−4, 3) → (4, 3)

sadsdda

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.