Answer:
PS=
![√(26)units](https://img.qammunity.org/2020/formulas/mathematics/high-school/ool5lnapk336pvhf8fg8i1afjbhcukd1ul.png)
Explanation:
Given : PQRS is a trapezoid on a coordinate plane P(7,4) Q(10,4) R(13,-1) S(8,-1).
To find:: Length of the side PS
Solution : Using the distance formula, we can find the length of the side PS, therefore
PS=
![\sqrt{(y_(2)-y_(1))^2+(x_(2)-x_(1))^2}](https://img.qammunity.org/2020/formulas/mathematics/high-school/27pmdc7ms3foaz0upueujvd8e04j65rsar.png)
PS=
![\sqrt{(-1-4)^(2)+(8-7)^2 }](https://img.qammunity.org/2020/formulas/mathematics/high-school/6y0xfef79y1oxdfenkowt6teox7d9cnx82.png)
PS=
![√((-5)^2+(1)^2)](https://img.qammunity.org/2020/formulas/mathematics/high-school/ufsckpbvh5vnr9o1uj4ew2u6b8ayps3p1h.png)
PS=
![√(25+1)](https://img.qammunity.org/2020/formulas/mathematics/high-school/mkggehz43z5n5g5n8eizcgtdd27e65kl50.png)
PS=
![√(26)units](https://img.qammunity.org/2020/formulas/mathematics/high-school/ool5lnapk336pvhf8fg8i1afjbhcukd1ul.png)
which is the required length of the side PS.