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?

1 Answer
Jun 6, 2018

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)#