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

Answer:

Option B

Step-by-step 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'=$\frac{11-6}{6-4} =\frac{5}{2}\\\\\frac{6-1}{4-2}= \frac{5}{2}$

= slope of OA

Thus option B satisfies both

So answer is B