Question

suppose that a=(3, 2) are the coordinates of a point in the xy - plane.
a) find the coordinates of the point if a is shifted 3 units to the right and 1 unit down.
b) find the coordinates of the point if a is shifted 1 unit to the left and 5 units up.
a) the coordinates of the point are if a is shifted 3 units to the right and 1 units down.
(simplify your answer. type an ordered pair.)

Explanation:

Step1: Shift x - coordinate for right - shift

For a right - shift of 3 units, we add 3 to the x - coordinate of the point A(3, 2). The original x - coordinate is 3, so the new x - coordinate is \(3 + 3=6\).

Step2: Shift y - coordinate for down - shift

For a down - shift of 1 unit, we subtract 1 from the y - coordinate of the point. The original y - coordinate is 2, so the new y - coordinate is \(2-1 = 1\).

Step3: Shift x - coordinate for left - shift (for part b)

For a left - shift of 1 unit in part b, we subtract 1 from the x - coordinate of the point A(3, 2). The new x - coordinate is \(3-1 = 2\).

Step4: Shift y - coordinate for up - shift (for part b)

For an up - shift of 5 units in part b, we add 5 to the y - coordinate of the point. The new y - coordinate is \(2 + 5=7\).

Answer:

a) (6, 1)
b) (2, 7)