\( \begin{array}{llll}\text { a. } & \mathrm{P}=(1 / 2 ; 1 / 2) & \mathrm{Q}=(1 / 2,5 / 2) & \mathrm{R}=(13 / 4,1 / 2) \\ \text { b. } & \mathrm{T}=(-3 / 4,0) & \mathrm{U}=(5 / 2,0) \quad \mathrm{V}=(3 / 4,7 / 2) \\ \text { c. } & \mathrm{X}=(1 ;-1 / 2) \quad \mathrm{Y}=(-3 / 2,1 / 4) \quad \mathrm{Z}=(5 / 2,1 / 2) \\ \text { d. } & \mathrm{A}=(-5 / 2 ;-5 / 2) \quad \mathrm{B}=(7 / 4 ;-5 / 2) \quad \mathrm{C}=(7 / 4 ; 5 / 4)\end{array} \)

Here's a fun fact: Did you know that coordinates like the ones you've provided can represent points in the Cartesian plane, which is a groundbreaking concept introduced by René Descartes in the 17th century? This system allows us to express geometric shapes and equations in a mathematical format, making it crucial for the development of modern geometry and algebra! Now, let’s talk about the practicality of using these coordinates in real life. You can think of GPS location services! When you input coordinates into your GPS, it tells you precisely where to go. Just like you have points \(P\), \(Q\), and others, GPS systems use latitude and longitude (just like your x and y coordinates) to pinpoint exact locations on Earth, guiding us on our adventures.