Question

A rectangular room has coordinates Q(2, 2), R (7, 2), S(7, 5), and T(2, 5) on the blueprint. The homeowner wants this room to be 25% larger. What are the coordinates of the new room?

Answer 1

A few ambiguities in this problem. Clearly we're to dilate but it's not clear around which point. It's not clear if we're to scale the linear dimensions by `5/4` -- maybe 25% larger refers to the area or the volume.

Disambiguating, let's say we'll keep Q the same and scale the linear dimensions, so we dilate by `5/4` around Q.

We translate each point to the origin by subtracting `(2,2)`, then we scale by `5/4`, then we translate back:

`(2,2) to 5/4( (2,2)-(2,2)) + ( 2,2) = (2,2)`

`(7,5) to 5/4( (7,5)-(2,2)) + ( 2,2) = (33/4,23/4)`

The rest don't require calculation:

`(7,2) to (33/4,2)`

`(2, 5) to (2,23/4)`