Question

Calculate the possible values for missing value (2, 19) (32, y) given the distance of 34

Answer 1

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{19})\qquad (\stackrel{x_2}{32}~,~\stackrel{y_2}{y})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ \stackrel{d}{34}=√((32-2)^2 + (y-19)^2)\implies 34^2=(32-2)^2 + (y-19)^2 \\\\\\ 1156=30^2 +(y-19)^2\implies 1156=900 + (y-19)^2\implies 256=(y-19)^2 \\\\\\ \pm√(256)=\pm√((y-19)^2)\implies \pm 16=\pm (y-19)\implies \mp 16 =y - 19 \\\\\\ \mp 16 + 19 = y\implies y= \begin{cases} 3\\ 35 \end{cases}`