Step: 1

Scale factor = A'B' AB

= 8 12 = 2 3

[Substitute the values and simplify.]

Step: 2

The scale factor is 2 3 .

Correct Answer is : 2 3

Step: 1

Since the center of dilation is A, the image of A will be A itself. i.e., A and A′ coincides.

Step: 2

When B is dilated by scale factor of 2 with A as center, B will be the midpoint between A′ and B′.

Step: 3

Coordinates of B′ are (- 7, 6)

[Apply midpoint formula.]

Step: 4

When C is dilated by scale factor of 2 with A as center, C will be the midpoint between A′ and C′.

Step: 5

Coordinates of C′ are (- 9, - 6)

[Apply midpoint formula.]

Step: 6

A′B′C′ is plotted as shown in Figure 1.

Correct Answer is : Figure 1

Step: 1

Step: 2

Image of A is A itself. A and A′ coincides.

Step: 3

Image of B is B′. A B ′ A B = 3

Step: 4

B divides AB′ in the ratio 1: 2

Step: 5

Coordinates of B′ are (8, 0).

Step: 6

Image of C is C′. A C ′ A C = 3

Step: 7

Coordinates of C′ are (5, 9).

[Line segment formula.]

Correct Answer is : A′(2, 0), B′(8, 0) and C′(5, 9)

Step: 1

P and Q are (2, 4) and (6, 9)

[Given.]

Step: 2

P′ = (1, 2)

[Multiply the coordinates by the scale factor.]

Step: 3

Q′ = (2, 3)

[Multiply the coordinates by the scale factor.]

Step: 4

PQ = [( 6 - 2 ) ² + ( 9 - 4 ) ² ] ]

[Distance formula.]

Step: 5

= 4 1

[Simplify.]

Step: 6

P′Q′ = [( 2 - 1 ) ² + ( 3 - 2 ) ² ]

[Distance formula.]

Step: 7

P′Q′ = 2

[Simplify.]

Step: 8

PQ - P′Q′ = 4 1 - 2

[Steps 5 and 7.]

Correct Answer is : 4 1 - 2

Step: 1

Point V is (2, 1)

Step: 2

When it is under dilation with a scale factor of 4.5, the image will be (2 × 4.5, 1 × 4.5) = (9, 4.5)

Step: 3

This point is shown as D in the picture.

Correct Answer is : D

Step: 1

Line segment O-V-R is dilated under a scale factor of 1.5 with origin as the center.

[Given]

Step: 2

Co-ordinates of points O, V and R are (0, 0), (2, 4) and (4, 8) respectively.

Step: 3

To find the image of a point on the coordinate plane under a dilation with center as origin, multiply the co-ordinates with the scale factor.

Step: 4

Image of V (2, 4) = (2 × 1.5, 4 × 1.5)

Step: 5

= (3, 6)

[Simplify]

Step: 6

Therefore, co-ordinates of the point V after dilation is (3,6).

Correct Answer is : (3, 6)

Step: 1

Quadrilateral ABCD is the dilation of quadrilateral PQRS under a scale factor of 1 2

[Given.]

Step: 2

AB | | PQ

[Given.]

Step: 3

Images of vertices P, Q, R and S after dilation are A, B, C and D respectively.

Step: 4

So, AD || PS

[Parallelism of lines of a figure does not change under dilation.]

Correct Answer is : PS

Step: 1

Triangle PQR is dilated under a scale factor of 2 with origin as the center of dilation.

[Given.]

Step: 2

Images of vertices P, Q and R after dilation are P′, Q′, and R′ respectively.

[Orientation, i.e. the lettering order of a figure does not change under dilation.]

Step: 3

The triangle P′Q′R′ is the dilation of the triangle PQR with respect to the origin.

Step: 4

Therefore, figure 2 represents the dilation of the triangle PQR.

Correct Answer is : Figure 2

Step: 1

Line segment O-A-P is dilated under a scale factor of 0.5 with origin as the center.

[Given.]

Step: 2

Co-ordinates of points O, A and P are (0, 0), (-4, 2) and ( - 10, 5) respectively.

Step: 3

To find the image of a point on the coordinate plane under a dilation with center as origin, multiply the co-ordinates with the scale factor.

Step: 4

Image of A (- 4, 2) = (- 4 × 0.5, 2 × 0.5)

Step: 5

(-2, 1)

Step: 6

Image of P ( - 10, 5) = (- 10 × 0.5, 5 × 0.5)

Step: 7

( - 5, 2.5)

Step: 8

We notice that the points O, A′ and P′ are collinear

Step: 9

Therefore, the points O, A′ and P′ are collinear

Correct Answer is : Collinear

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