(03.01 mc)

triangle abc is translated by the rule (x + 1, y + 1) and then dilated by a scale factor of 2 centered at the origin. which statement describes the properties of triangles abc and a''b''c'' after the transformations?

a. ∠c and ∠c'' are congruent after both the translation and the dilation.

b. ∠c and ∠c'' are congruent after the dilation, but not after the translation.

c. segment ac and segment a double prime c double prime are congruent after both the translation and the dilation.

d. segment ac and segment a double prime c double prime are congruent after the dilation, but not after the translation.

Option A. ∠C and ∠C'' are congruent after both the translation and the dilation

Step-by-step explanation:

we know that

The translation is a rigid transformation. After the translation the image and the pre-image are congruent

The dilation is a non rigid transformation. After the dilation the image and the pre-image are similar

Remember that

If two figures are similar, then its corresponding angles are congruent and the ratio of its corresponding sides is proportional

If two figures are congruent, then its corresponding angles and corresponding sides are congruent

therefore

∠C and ∠C'' are congruent after both the translation and the dilation

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus