Triangle pqr is translated by the rule (x − 1, y − 1) and then dilated by a scale factor of 3 centered at the origin. which statement describes the properties of triangles pqr and p''q''r'' after the transformations? ∠p and ∠p'' are congruent after the translation, but not after the dilation. ∠p and ∠p'' are congruent after the dilation, but not after the translation. segment pq and segment p double prime q double prime are congruent after the translation, but not after the dilation. segment pq and segment p double prime q double prime are congruent after the dilation, but not after the translation

  segment PQ and segment P double prime Q double prime are congruent after the translation, but not after the dilation

Step-by-step explanation:

Translation and dilation have no effect on angles. All angles are congruent after either or both of translation and dilation.

Translation has no effect on size, so segments are congruent after translation. Dilation changes size, so segments are not congruent after dilation.

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Comment on the problem wording

Ordinarily, the first transformation (translation) would result in figure P'Q'R', so P'Q' would be congruent to PQ. Then the second transformation (dilation) would change figure P'Q'R' to figure P''Q'' R'', which is no longer congruent to either figure P'Q'R' or figure PQR.

That is, talking about "segment P double prime Q double prime ... after the translation, but not the dilation" makes no sense, because there is no such segment. The segment that exists after the translation, but not the dilation, is segment P'Q'.

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.