There are three kinds of isometric transformations of 2D shapes.
A translation is transformation in which every point of figure moves a fixed distance in a given direction.
Rotating the shape means moving them around a fixed point. There are two directions
i) Clockwise
ii) Counter clockwise (or) Anti clockwise
The shape itself stays exactly the same, but its position in the space will change.
90° clockwise 90° counter clockwise 180° 270° clockwise 270° counter clockwise |
(x, y) ==> (y, -x) (x, y) ==> (-y, x) (x, y) ==> (-x, -y) (x, y) ==> (-y, x) (x, y) ==> (y, -x) |
The reflected image will be congruent to the original.
What is line of reflection ?
A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.
Reflections can be performed easily in the coordinate plane using the general rules below.
Types of reflectionsReflection over x axis Reflection over y axis Reflection over y = x Reflection over y = -x Reflection about origin |
Rules(x, y) ==> (x, -y) (x, y) ==> (-x, y) (x, y) ==> (y, x) (x, y) ==> (-y, -x) (x, y) ==> (-x, -y). |
The object A has been translated to give an image B in each diagram. Give the translation in each case.
Problem 1 :
Solution :
Observing the vertex of A to vertex of rectangle B, only horizontal movement is done.
Moved 4 units right, so the required translation vector is (4, 0).
Problem 2 :
Translate the shape 2 units right and 1 unit up.
Solution :
Writing the vertices,
U (-3, 0), Z (-2, 3), F (1, 3) and H (1, 1)
We translate the figure 2 units right and 1 unit up. So,
(x, y) ===> (x + 2, y + 1)
U (-3, 0) ==> U' (-3+2, 0+1) ==> U' (-1, 1)
Z (-2, 3) ==> Z' (-2+2, 3+1) ==> Z' (0, 4)
F (1, 3) ==> Z' (1+2, 3+1) ==> F' (3, 4)
H (1, 1) ==> H' (1+2, 1+1) ==> Z' (3, 2)
Problem 3 :
Rotation 90° clockwise about the origin.
Solution :
Marking the coordinate,
Z (0, -4), J (0, -5), T (4, -3) and S (3, -5)
Rotation ==> 90° clockwise
Rule :
(x, y) ==> (y, -x)
Z (0, -4) ==> Z' (-4, 0)
J (0, -5) ==> J' (-5, 0)
T (4, -3) ==> T' (-3, -4)
S (3, -5) ==> S'(-5, -3)
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