Question

The vertices of a rectangle are R(-5, -5), S(-1,-5), 7(-1, 1), and U(-5, 1). After translation,

R' is the point (-11, -11). Find the translation rule and coordinates of U'.

(x, y) + (x - 6, y + 6); (-11, 7)

(x, y) (x - 6, y - 6); (-11,-5)

(x,y) → (x + 6, y - 6); (1, -5)

(x, y) + (x + 6, y + 6); (1,7)

Answer 1

B. (x, y) (x - 6, y - 6); (-11,-5)

Explanation:

Given the vertices of a rectangle are R(-5, -5), S(-1,-5), 7(-1, 1), and U(-5, 1). After translation, the coordinate R' is at the point (-11, -11), in order to know the translation factors used;

Let (x, y) be the translation coordinate added to the original coordinate R to get R'. To get the coordinate (x, y)

(x, y)+(-5, -5) =(-11, -11)

x - 5 = -11

x = -11+5

x = -6

Similarly;

y-5 = -11

y = -11+5

y = -6

Hence the coordinates added to initial vertices is (-6, -6)

To get the new coordinate U' after translation, we will add the coordinate (-6, -6) to the U(-5, 1) as shown;

(x, y) + (-5, 1) = (-6, -6)+(-5, 1)

= (-6-5, -6+1)

= (-11, -5)

Hence the coordinates of U' is (-11, -5) and the translation rule is (- 6+ x, -6+y) where (x, y) is (-6, -6).

Based on the above calculation, it can be seen that (x, y) (x - 6, y - 6); (-11,-5) is correct.