Question

Predict what would happen to the coordinates at a point (x, y) as the point translates to produce point (x’, y’). Assume that the point translates a units to the left or right and b units up or down. Express your answers in terms of x, y, a, and b. Be sure to watch your signs.

Answer 1

Answer:

Displacement x′ y′

up                    x y + b

down                 x y − b

right                 x + a y

left                          x - a y

Step-by-step explanation:

Answer 2

Answer:

(x', y') = (x+a, y+b)

Step-by-step explanation:

x-coordinates increase the farther to the right you go. If you go "a" units to the right of where you were, the x-coordinate increases by "a".

Likewise, y-coordinates increase the farther up you go. If you go "b" units up from where you were, the y-coordinate increases by "b".

If "a" and "b" are the amounts a point (x, y) is translated to the right and up, respectively, then the new point (x', y') has coordinates ...

(x', y') = (x +a, y +b)

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"a" and "b" can be signed numbers. When either is negative, it corresponds to movement in the direction opposite to right or up, respectively.