Triangle abc is translated 2 units right and 5 units down to form triangle a′b′c′. this triangle is then translated 5 units right and 4 units up to form triangle a″b″c″. if vertex a is at (-4, 2), what are the coordinates of vertex a″?

The coordinates of vertex A" is (3 , 1)

Step-by-step explanation:

* Lets revise The translation of a point

- If the point (x , y) translated horizontally to the right by h units

 then the new point = (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then the new point = (x - h , y)

- If the point (x , y) translated vertically up by k units

 then the new point = (x , y + k)

- If the point (x , y) translated vertically down by k units

 then the new point = (x , y - k)

* Now lets solve the problem

∵ Δ ABC has a vertex A = (-4 , 2)

∵ The Δ ABC is translated 2 units right and 5 units down to form

   triangle A′B′C′

- From the rule above the x coordinate id added by 2 and the

 y-coordinate is subtracted by 5

∴ A' = (-4 + 2 , 2 - 5) = (-2 , -3)

∴ The image of vertex A is A' = (-2 , -3)

∵ Δ A'B'C' is then translated 5 units right and 4 units up to form

   triangle A″B″C″

- From the rule above the x coordinate is added by 5 and the

 y-coordinate is add by 4

∴ A" = (-2 + 5 , -3 + 4) = (3 , 1)

* The coordinates of vertex A" is (3 , 1)

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.