Find the distance $d$ between the points $( -3,5)$ and $( 3,2) .$

Solution We use the distance formula with $P_{1}= ( x_{1}, y_{1}) =( -3,5)$ and $P_{2}= ( x_{2}, y_{2}) =( 3,2) .$ $$d=\displaystyle\sqrt{ [ 3-( -3) ] ^{2}+( 2-5) ^{2}}=\displaystyle\sqrt{ 6^{2}+( -3) ^{2}}=\displaystyle\sqrt{36+9}=\displaystyle\sqrt{45}=3\displaystyle\sqrt{5}\approx 6.708$$