Which transformation is shown by the coordinates below? L (-1, 9) M (-8, 8) N (-3, 5) L '(- 9, -1) M' (- 8, -8) N '(- 5, -3) A. Reflection over the x-axis / B. Translation 8 units left and 8 units down / C. Rotation 90 degrees clockwise / D. Rotation 270 degrees clockwise

D. Rotation 270 degrees clockwise.

Step-by-step explanation:

The transformation used in the coordinates below was a rotation 270 degrees clockwise, whose definition is:

Please note that clockwise rotation is represented by the minus sign.

Where is the norm of original point, defined as:

,

And is the direction of the point centered at origin and with respect to +x semiaxis, measured in sexagesimal degrees:

Now we proceed to prove the statement:

Norm

Direction

The point is located on 2nd quadrant, which means that . Then:

Rotation

Norm

Direction

The point is located on 2nd quadrant, which means that . Then:

Rotation

Norm

Direction

The point is located on 2nd quadrant, which means that . Then:

Rotation

Hence, the correct answer is D.

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.

which expression represents the approximate length of bc?

step-by-step explanation: