Question

Which of the following is true?

1. The scale factor is 5/2 with a center of dilation at point B. The image of AB is on the same line because it passes through the center of dilation and CD is parallel to its image because it does not pass through the center of dilation.

2. The scale factor is 5/2 with a center of dilation at point B. The image of AB is on the same line because it does not pass through the center of dilation and CD is parallel to its image because it does pass through the center of dilation.

3. The scale factor is 2/5 with a center of dilation at point B. The image of AB is on the same line because it does not pass through the center of dilation and CD is parallel to its image because it does pass through the center of dilation.

4. The scale factor is 2/5 with a center of dilation at point B. The image of AB is on the same line because it passes through the center of dilation and CD is parallel to its image because it does not pass through the center of dilation.

Answer 1

Option A

Explanation:

If the quadrilateral ABCD is dilated by a scale factor 'k' to form quadrilateral A'B'C'D',

Scale factor =
`\frac{\text{Length of one side of the Image}}{\text{Length of one side of the original}}`

k =
`(BA')/(BA)`

Distance between B(2, -5) and A(-1, -1) =
`√((x_2-x_1)^2+(y_2-y_1)^2)`

=
`√((2+1)^2+(-5+1)^2)`

= 5 units

Distance between B(2, -5) and A'(-5.5, 5) =
`√((-5.5-2)^2+(5+5)^2)`

=
`√((-7.5)^2+(10)^2)`

= 12.5 units

Scale factor 'k' =
`(12.5)/(5)`

k =
`(5)/(2)`

Therefore, ABCD is dilated by a scale factor
`(5)/(2)` about point B.

BA and it's image BA' are on the same line and passes through center of dilation B.

Similarly, lines CD and C'D' will be parallel because they do not pass through center of dilation.

Therefore, Option (A) will be the correct option.