Count to the right 4 units from point A(-3, 2).

Graph A'.

The coordinates of A' are (1, 2).

The x and y coordinates of its image P′ become (x - 3) and (y - 2), respectively.

So, the rule for the translation is (x, y) → (x - 3, y - 2).

The x-coordinate of the image P′ is negative.

So, the point P has been translated to the left.

Number of units, it has been translated left = 5 - (- 2) = 7 units

So, the point P has been translated up.

Number of units, it has been translated up = 9 - 5 = 4 units

So, the rule for the translation is (x, y) → (x - 7, y + 4).

The coordinates before translation and after translation are (- 2, 3) and (2, 3).

The x-coordinate after translation is greater than that before translation but the y-coordinate is not changed. So, the translation is towards right.

Translation = 2 - (- 2) = 2 + 2 = 4 units right.

So, move 4 units right from (- 2, 3) to reach (2, 3).

The coordinates of the line segment are (7, 6) and (3, -8).

The translation is done by 7 units left.

Since, the translation is done to left, the y-coordinate does not change.

7 - 7 = 0 and 3 - 7 = -4.

The new coordinates of the line segment are (0, 6) and (-4, -8).

After the first translation, 2 units right and 5 units up, the x-coordinate becomes 3 + 2 = 5 and y-coordinate becomes 4 + 5 = 9 units.

The coordinates after the first translation is (5, 9).

Again the image is translated, 2 units left and 1 unit down, the x-coordinate becomes 5 - 2 = 3 and y-coordinate becomes 9 -1 = 8.

The coordinates of the point after translation is (3, 8).

The two points are (4, 5) and (9, 5).

As the y-coordinate is not changing and the x-coordinate is positive and increasing, the translation is towards right.

The translation of the point is 9 - 4 = 5 units to the right.

So, to translate the point D(4, 5), to coordinates D′(9, 5), move 5 units right.

The point P is at (- 4, 2).

When the point is translated 3 units to the right the x-coordinate changes, but the y-coordinate remains the same.

After translation the x-coordinate becomes - 4 + 3 = - 1

The new coordinates of the point P after translation is (- 1, 2)

The horizontal change is the change in x-coordinate.

The horizontal change is 10.

Since the x-coordinate of the point K' is less than the x-coordinate of the point K, the horizontal translation is 10 units to the left from the point K.

When (- 2, 2) is translated down 3 units, the y-coordinate becomes - 1, but the x-coordinate remains same.

After translating (- 2, - 1) to 6 units right, the x-coordinate of the point becomes 4, but the y-coordinate remains same.

So, the coordinates of the new point C′ are (4, - 1).

Plot the point O (0, 0).

Count down 2 units and right 5 units from the point O.

Graph O′.

The coordinates of the image O′ are (5, - 2).

The x-coordinate of the image P′ is negative.

So, the point P has been translated to the left.

Number of units, it has been translated left = 8 - (- 3) = 11 units

The y-coordinate of the image P′ is greater than that of the point P.

So, the point P has been translated up.

Number of units it has been translated up = 13 - 7 = 6 units

So, the rule for the translation is (x, y) → (x - 11, y + 6).

A transformation in which every point of the figure moves the same distance and in the same direction is called translation or sliding.

Among the 3 figures, Figure 1 represents the slide of the figure(A).

Plot the point B (3, 5).

Count 3 units right and 5 units up from the point B.

Graph the points.

Therefore, the coordinates of the image of point B = (6, 10 )

After the first translation, 3 units right and 7 units up, the x-coordinate becomes 4 + 3 = 7 and y-coordinate becomes 6 + 7 = 13 units.

The coordinates after the first translation is (7, 13).

Again the image is translated 2 units left and 1 unit down, the x-coordinate becomes 7 - 2 = 5 and y-coordinate becomes 13 -1 = 12.

The coordinates of the point after translation is (5, 12).