CORE Coordinate Geometry and Transformations - New Indian ...

(i) Translation of a point P (x, y) to P’ (x + a , y + a)
x
y
x + a
y + a
Thus, point P(x, y)
P‟(x + a, y + a), where a is a constant.
So, if a = 2, then the point P(4, 7) is translated to P‟ (4 + 2, 7 +2) i.e., Q(6, 9)
Similarly, Q (-5, 9) is translated to Q‟ (-5 + 2, 9 +2) i.e., Q‟ (-3, 11)
PP‟ = =
QQ‟ = =
Thus, PP‟ = QQ‟
From the above, we observe that:
Each point is translated to a distance of or 2 in the plane in a fixed direction.
In general, when x x + a, y y + a
i.e., P(x, y) P(x + a, y + a), then distance translated = = in a fixed
direction.
Here in this case, fixed direction is = = 1 i.e. m = tan45 0 or tan135 0
Thus, direction is at an angle of 45 o or 135 o with x-axis.
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