Using the Distance Formula

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 \(P_{2}= ( x_{2}, y_{2}) =( 3,2) .\) \[ d=\displaystyle\sqrt{ [ 3-( -3) ] ^{2}+( 2-5) ^{2}}=\displaystyle\sqrt{ 6^{2}+( -3) ^{2}}=\displaystyle\sqrt{36+9}=\displaystyle\sqrt{45}=3\displaystyle\sqrt{5}\approx 6.708 \]