△xyz is mapped to △x'y'z' using the rules (x, y)→(x+5, y−3) followed by (x, y)→(−x, −y) . which statement describes the relationship between △xyz and △x'y'z'? △xyz is congruent to △x'y'z' because the rules represent a translation followed by a rotation, which is a sequence of rigid motions. △xyz is not congruent to △x'y'z' because the rules do not represent a sequence of rigid motions. △xyz is congruent to △x'y'z' because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions. △xyz is congruent to △x'y'z' because the rules represent a rotation followed by a translation, which is a sequence of rigid motions.

Given that △XYZ is mapped to △X'Y'Z' using the rules (x, y)→(x+5, y−3) followed by (x, y)→(−x, −y) .

We know that (x,y) => (x+h,y+k) type operation represents translation so rule (x, y)→(x+5, y−3)  will cause translation.

We know that (x,y) => (-x,-y) type operation represents rotation about origin so rule (x, y)→(−x, −y) will cause rotation.

So combining both results and comparing with given choices. we find that only 1st choice "△XYZ is congruent to △X'Y'Z' because the rules represent a translation followed by a rotation, which is a sequence of rigid motions."

is correct.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

sinn is the total amount of students now and m were the students before, you subtract them both (n-m) and divide that by m. then, since to get a percentage from a fraction you have to multiply by 100, your answer should look like this: n-m/m*100

step-by-step explanation: