Question

PLEASE HELP ASAP! Point B has the coordinates (1,2). The x-coordinate of Point A is -5. The distance between Point A and Point B is 10 units. What are the possible coordinates of Point A?

Answer 1

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-5}~,~\stackrel{y_1}{y})\qquad B(\stackrel{x_2}{1}~,~\stackrel{y_2}{2})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ 10= √((~~ 1- (-5) ~~)^2 + (~~ 2- y ~~)^2) \implies 10^2= (~~ 1 +5 ~~)^2 + (~~ 2 -y ~~)^2 \\\\\\ 100=36+(4-4y+y^2)\implies 100=y^2-4y+40 \\\\\\ 0=y^2-4y-60\implies 0=(y-10)(y+6)\implies y= \begin{cases} 10\\ -6 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-5~~,~~10)\hspace{5em}(-5~~,~-6)~\hfill`