Question

A design was constructed by using two rectangles, ABCD and A'B'C'D'. RectangleA'B'C'D' is the result of a translation of rectangle ABCD. The table of translations isshown below. Find the coordinates of point B.

Answer 1

From the table, to transform points in rectangle ABCD into A'B'C'D', we have to apply the next rule: (x, y) → (x+1, y-3). That is,

A(2, 4) → (2+1, 4-3) → A'(3, 1)

C(2, -1) → (2+1, -1-3) → C'(3, -4)

D(-6, -1) → (-6+1, -1-3) → D'(-5, -4)

Then, if we want to transform a point in A'B'C'D', the rule is: (x,y) → (x-1, y+3). Applying this rule to point B', we get:

B'(-5, 1) → (-5-1, 1+3) → B(-6, 4)