In a video game, a rectangular map has vertices M (10, 10), N (10, 20), P (40, 20), and Q (40, 10). When a player clicks the map, it is enlarged by a scale factor of 4.5 with the origin as the center of dilation. The new coordinates are:

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.

the distance between the school and her home is 3.6km.

explanation

12 mins = 0.2 hours = 1/5 hour

54 ÷ 3 = 18km per hour

1/5 of 18 = 3.6km per 12 mins