Which of the following represents the translation of D(−5,4) along vector <6,−8> and its reflection across the y-axis?

Answer:D (-5 , 4) → D' (1 , -4) → D" (-1 , -4) ⇒ 2nd answerStep-by-step explanation:* Lets revise some transformation- If the point (x , y) translated horizontally to the right by h units  ∴ Its image is (x + h , y)- If the point (x , y) translated horizontally to the left by h units  ∴ Its image is (x - h , y)- If the point (x , y) translated vertically up by k units  ∴ Its image is (x , y + k)- If the point (x , y) translated vertically down by k units  ∴ Its image is(x , y - k)- If point (x , y) reflected across the x-axis  ∴ Its image is (x , -y)- If point (x , y) reflected across the y-axis  ∴ Its image is (-x , y)* Now lets solve the problem- The point D is (-5 , 4)- The vector of the translation is <6 , -8>∵ 6 is positive number∴ Point D will translate horizontally 6 units to the right∵ x-coordinate of D = -5- Add the x-coordinate of D by 6 to find the x-coordinate of D'∴ The x-coordinate of D' = -5 + 6 = 1∴ The x-coordinate of D' = 1∵ -8 is negative number∴ Point D will translate vertically 8 units down∵ y-coordinate of D = 4- Add the y-coordinate of D by -8 to find the y-coordinate of D'∴ The y-coordinate of D' = 4 + -8 = -4∴ The y-coordinate of D' = -4∴ The coordinates of D' are (1 , -4)- If point (x , y) reflected across the y-axis  then its image is (-x , y)∵ D' is reflected across the y-axis∵ D' = (1 , -4)- Change the sign of its x-coordinate∴ D" = (-1 , -4)∴ The coordinates of D" are (-1 , -4)* D (-5 , 4) → D' (1 , -4) → D" (-1 , -4)