Cartesian Plane, SMB-016 Calculate the value(s) of `p` given that the points `(p,3)` and `(1,p)` are exactly 10 units apart. (3 marks) --- 7 WORK AREA LINES (style=lined) --- Show Answers Only `p=9\ text{or}\ -5` Show Worked Solution `(p,3),\ \ (1,p)` `text{Using the distance formula:}` `d` `=sqrt{(x_2-x_1)^2+(y_2-y_1)^2}` `10` `=sqrt{(p-1)^2+(3-p)^2}` `10` `=sqrt{p^2-2p+1+9-6p+p^2}` `10` `=sqrt{2p^2-8p+10}` `100` `=2p^2-8p+10` `0` `=2p^2-8p-90` `0` `=p^2-4p-45` `0` `=(p-9)(p+5)` `:.p=9\ text{or}\ -5`