Step: 1

Count down 4 units and left 2 units from the point A.

Step: 2

Graph A′.

Step: 3

The coordinates of the image A′are (- 4, - 2).

Correct Answer is : (- 4, - 2)

Step: 1

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

[The point P (x , y ) is moved 3 units to left and 2 units down.]

Step: 2

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

Correct Answer is : (x , y ) → (x - 3, y - 2)

Step: 1

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

Step: 2

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

Step: 3

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

Step: 4

Step: 5

So, the point P has been translated up.

Step: 6

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

Step: 7

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

Correct Answer is : (x , y ) → (x - 7, y + 4)

Step: 1

[Original line equation.]

Step: 2

The line has been translated 3 units left and 3 units up.

Step: 3

Step: 4

(y - 3) = 6(x + 3) + 5

[Replace x with (x + 3) and y with (y - 3).]

Step: 5

[Distribute.]

Step: 6

Step: 7

[Simplify.]

Step: 8

So, equation of the image of the line is y = 6x + 26.

Correct Answer is : y = 6x + 26

Step: 1

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

Step: 2

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

Step: 3

Number of units, it has been translated right = 7 - 5 = 2 units.

Step: 4

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

Step: 5

So, the point P has been translated down.

Step: 6

Number of units, it has been translated down = 3 - (- 2) = 5 units.

Step: 7

So, the rule is (x , y ) → (x + 2, y - 5).

Correct Answer is : (x , y ) → (x + 2, y - 5)

Step: 1

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

Step: 2

After translating (- 1,- 1) to 5 units right, the x -coordinate of the point becomes 4, but the y-coordinate remains same.

Step: 3

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

Correct Answer is : (4, - 1)

Step: 1

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

Step: 2

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

Step: 3

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

Step: 4

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

Correct Answer is : Move 4 units right.

Step: 1

When a point is reflected over a vertical line the y -coordinate remains the same.

Step: 2

The point P(- 2, - 4) is reflected over the line x = 4.

Step: 3

The distance of the point from the line x = 4 is 2 + 4 = 6.

Step: 4

So, the image of the point will be 6 units away from the line x = 4.

Step: 5

The x -coordinate of the image of the point with respect to the coordinate axes = 6 + 4 = 10.

Step: 6

So, the coordinates of the image of the point P(- 2, - 4) along x = 4 are (10, - 4).

Correct Answer is : (10, - 4)

Step: 1

When a point is reflected over a horizontal line, the x -coordinate remains the same.

[The line y = 5 will be parallel to the x -axis.]

Step: 2

The point W (- 2, - 2) is reflected over the line y = 5.

Step: 3

The distance of the point (- 2, - 2), from the line y = 5 is 2 + 5 = 7 units

Step: 4

So, the image of the point will be 7 units away from the line y = 5.

Step: 5

The y -coordinate of the image = 7 + 5 = 12

Step: 6

So, the coordinates of the image are (- 2, 12).

Correct Answer is : (- 2, 12)

Step: 1

When point is rotated by 180^{o}, only the signs of the x and the y -coordinates will be interchanged.

Step: 2

Represent the horizontal and the vertical distances of the point P(2, 4) as a rectangle.

Step: 3

Now tilt the rectangle by 180^{o} as the point has to be rotated by 180^{o}.

Step: 4

The coordinates of point C after rotating 180^{o} are C'(-2, -4).

[Observe that the signs of the x and the y -coordinates are interchanged.]

Correct Answer is : (-2, -4)

Step: 1

Figure-2 represents the mirror image of Figure-1.

Step: 2

The transformation used in the Figure-1 to change as Figure-2 is 'reflection'.

Step: 3

So, the correct choice is reflection.

Correct Answer is : Reflection

Step: 1

Count down 4 units and left 2 units from the point A.

Step: 2

Graph A′.

Step: 3

The coordinates of the image A′ are (- 4, - 2).

Correct Answer is : (- 4, - 2)

Step: 1

R (4, 8) is mapped to R′ (2, 4). Scale factor is 1 2 and center (0, 0).

Step: 2

V (1, 1) is mapped to V′(5, 5). Scale factor is 5 and center (0, 0).

Correct Answer is : R dilated by scale factor 1 2 , V dilated by scale factor 5, center of dilation (0, 0)

Step: 1

Represent the point P (3, 4) on the coordinate plane.

Step: 2

The point P (3, 4) is rotated counter clockwise by 180° as shown in the figure.

Step: 3

The coordinates of the point P after rotating 180° are P' (- 3, - 4).

Correct Answer is : P (- 3, - 4)

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