The endpoints of a segment are M(2,5) and N(8,-1). What are the new endpoints of it if it is translated

Complete Question

The endpoints of a segment are M(2,5) and N(8,-1). What are the new endpoints of it if it is translated along the vector <-2,3>

Step-by-step explanation:

From the question we are told that

Generally the translation along the vector <-2,3> is mathematically given as

Therefore

Generally  the new endpoints are are mathematically given

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