AMSCO'S Geometry. New York - Rye High School

Translations in the Coordinate Plane 235We can write Theorem 6.7 and its corollaries as a single statement. Under a translation, distance, angle measure, collinearity, and midpoint arepreserved.Let T a,bbe the symbol for a translation of a units in the horizontal directionand b units in the vertical direction. We can write:T a,b(x, y) (x a, y b)EXAMPLE 1The coordinates of the vertices of ABC are A(3, 3), B(3, 2), and C(6, 1).a. Find the coordinates of the vertices of ABC, the image of ABCunder T 5,3.b. Sketch ABC and ABC on graph paper.Solution a. Under the given translation, every b.point moves 5 units to the left and3 units up.A(3, 3) → A(3 5, 3 3) A(2, 0)B(3, 2) → B(3 5, 2 3) B(2, 5)C(6, 1) → C(6 5, 1 3) C(1, 4)yB(2, 5)1A(2, 0) OC(1, 4)B(3, 2)C(6, 1)1xA(3, 3)Translational SymmetryDEFINITIONA figure has translational symmetry if the image of every point of the figure is apoint of the figure.Patterns used for decorative purposes such as wallpaper or borders onclothing often appear to have translational symmetry. True translational symmetrywould be possible, however, only if the pattern could repeat without end.