Question

A dilation maps M (4, 2) to N (2, 1), what would the image of K (–2, 5) be under the same dilation?

• A. (-1, 2.5)
• B. (1, 2.5)
• C. (1, -2.5)
• D. (-1, -2.5)

Answer 1

The correct option is A

(-1, 2.5)

A dilation changes the distance between points by multiplying the x and y coordinates by the scale factor. The x coordinate for M is 4, and the x coordinate for N is 2 i.e. assuming a common scale factor k we get,

4k = 2

i.e. k = 1/2

Now, the point K (–2, 5) then becomes, (-1, 2.5)

So the image has the coordinates (-1, 2.5)