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)