If a translation takes triangle CAT to C'A'T', what is A'T'?
square route of 10
square route of 17
square route of 5
cannot be determined

square root of 10 units

Step-by-step explanation:

The complete question is

If a translation takes triangle CAT to C'A'T', what is A'T'?

Triangle CAT is shown. C is at 0, 0, A is at negative 2, 1, T is at negative 1, 4

we know that

A translation is a rigid transformation that produce congruent figures

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

In this problem

triangle CAT and triangle C'A'T' are congruent

so

CA≅C'A'

AT≅A'T'

CT≅C'T'

Find the distance AT

In this problem we have

A(-2,1) and T(-1,4)

the formula to calculate the distance between two points is equal to

substitute

therefore

step-by-step explanation:

it's is b

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1