Question

What is the transformation of A(4,6) when dilated with a scale factor of 2, using the point (2,1) as the center of dilation?

A. A '(0, -4)
B. A '(6, 11)
C. A '(8, 12)
D. A '(5, 8)

Answer 1

Option B

Explanation:

Given that the point A(4,6) is dilated with a scale factor of 2

about the point O(2,1) as centre of dilation

This implies that the new point A' will lie on the lineOA with distance equal to double of OA.

Or A will be the mid point of OA' and AA' will have same slope as OA

Considering the above two conditions we find that

Option A cannot be right.

Option B: Midpoint of OA' = (4,6) matches with given

Slope of AA'=
`(11-6)/(6-4) =(5)/(2)\\\\(6-1)/(4-2)= (5)/(2)\`

= slope of OA

Thus option B satisfies both

So answer is B