Line ab has a length of 5 cm. the line segment is dilated to produce line a'b', which has a length of 2 cm. find the scale factor of the dilation.

a. k = 2/5
b. k = 1/2
c. k = 5/2
d. k = 2

you in advance for your !

Option A is correct

k = 2/5

Step-by-step explanation:

The rule of dilation with scale factor k is given by:

As per the statement:

Line AB has a length of 5 cm. The line segment is dilated to produce line A'B', which has a length of 2 cm.

⇒original Length (AB)= 5 cm

and

Image length (A'B') = 2 cm

Apply the rule of dilation we have;

Substitute the given values;

Therefore, the scale factor of the dilation is, 2/5

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.