Question

A rectangular room has coordinates Q(2, 4), R(5, 4), S(5, 6), and T(2, 6) on the blueprint. The homeowner wants the dimensions of this room to be 25% larger. What are the coordinates of the new room?

Answer 1

To enlarge the room by 25%, we apply a scale factor of 1.25 to the original length and width, yielding new dimensions. The new coordinates are Q'(2, 4), R'(5.75, 4), S'(5.75, 6.5), and T'(2, 6.5), keeping the bottom left corner at Q(2, 4) fixed.

To increase the dimensions of a rectangular room by 25%, you multiply the length and width by 1.25 (or the scale factor of 1.25). The original coordinates (Q, R, S, T) represent a room with a length of 3 units (from Q to R or S to T) and a width of 2 units (from Q to T or R to S). Multiplying each dimension by 1.25, we get the new length as 3.75 (3 x 1.25) and the new width as 2.5 (2 x 1.25).

The new coordinates, assuming the bottom left corner remains fixed at Q(2, 4), will be:

• Q'(2, 4), unchanged as it is the anchor point.
• R'(5.75, 4), calculated as 2 + 3.75 for the x-coordinate while y remains the same.
• S'(5.75, 6.5), calculated as 2 + 3.75 for the x-coordinate and 4 + 2.5 for the y-coordinate.
• T'(2, 6.5), y-coordinate calculated as 4 + 2.5 while x remains the same.

: The coordinates for the new, 25% larger room are Q'(2, 4), R'(5.75, 4), S'(5.75, 6.5), and T'(2, 6.5).