Which sequence of transformations will map figure h onto figure h′?

a. rotation of 180° about the origin, translation of (x + 10, y − 2), and reflection across x = −6
b. rotation of 180° about the origin, translation of (x + 10, y − 2), and reflection across y = −6
c. rotation of 180° about the origin, translation of (x − 10, y + 2), and reflection across y = −6
d. rotation of 180° about the origin, translation of (x − 10, y + 2), and reflection across x = −6

the solution is the point

step-by-step explanation:

we have

> equation a

> equation b

adds equation a and equation b

substitute the value of x in equation b to find the value of y

the solution is the point

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.