Polygon abcde is reflected across the x-axis to form polygon a′b′c′d′e′. then polygon a′b′c′d′e′ is dilated by a scale factor of 0.5 about d′ to form polygon lmnop. vertices a and b correspond to l and m, respectively. if the length of ab is 2.20 units, the length of lm units. write your answer as a decimal number to two decimal places.

Answer with explanation:

It is given that ,Polygon ABCDE is reflected across the x-axis to form polygon A′B′C′D′E′.

→→When a geometrical shape is reflected ,the two image that is polygon A′B′C′D′E′ and Pre image Polygon ABCDE  are Congruent to each other.

→→Also, Distance from line of Reflection that is from X axis to all the vertices of polygon ABCDE = Distance from line of Reflection that is from X axis to all the vertices of polygon A′B′C′D′E′.

⇒Polygon A′B′C′D′E′ is dilated by a scale factor of 0.5 about D′ to form polygon L M N OP.

Dilation Factor <1

So, →Size of polygon L M N OP <  Size of polygon A′B′C′D′E′

When a geometrical shape is dilated the two, polygon A′B′C′D′E′ and polygon L M N OP are similar to each other.

≡A→L, B→M

AB=2.20 Units

Corresponding Sides of two polygons that is , polygon A′B′C′D′E′ and polygon L M N OP, will be Proportional to each other which will be equal to Dilation factor.

⇒L M = 2.20 × AB

L M= 2.20 × 0.5

L M= 1.10 units

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option