The vertices of a polygon are given. Find the coordinates of the vertices of the image after the specified translation. P(–5, 4), Q(1, 4), R(1, 1);
(x, y) —--> (x + 1, y – 5)

P’ (__, __) Q’ (__,__) R’ (__,__)

The coordinates of the images are P' (-4, -1), Q' (2, -1), R' (2, -4)

Step-by-step explanation:

If the point (x, y) is translated horizontally h units and vertically k units, then its image is (x + h, y + k) and the rule of translation is T (x + h, y + k)

∵ The vertices of the polygons are P (-5, 4), Q (1, 4), R (1, 1)

∵ The rule of translation is (x, y) → (x + 1, y - 5)

→ That means add each x-coordinate by 1 and subtract each

   y-coordinate by 5

∴ P' = (-5 + 1, 4 - 5)

∴ P' = (-4, -1)

∴ Q' = (1 + 1, 4 - 5)

∴ Q' = (2, -1)

∴ R' = (1 + 1, 1 - 5)

∴ R' = (2, -4)

∴ The coordinates of the images are P' (-4, -1), Q' (2, -1), R' (2, -4)