Question

Point B has coordinates ​(2​,1​). The​ x-coordinate of point A is -10 . The distance between point A and point B is 13 units. What are the possible coordinates of point​ A?

Answer 1

hmmm we know B (2 , 1), and let's say the y-coordinate is "y" for A, so A (-10 , y).

$~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad A(\stackrel{x_2}{-10}~,~\stackrel{y_2}{y})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ BA=\sqrt{[-10 - 2]^2 + [y - 1]^2}\implies 13=\sqrt{(-12)^2+(y^2-2y+1)} \\\\\\ 13^2=(-12)^2+(y^2-2y+1)\implies 169=144+y^2-2y+1 \\\\\\ 169=y^2-2y+145\implies 0=y^2-2y-24 \\\\\\ 0=(y-6)(y+4)\implies y= \begin{cases} 6\\ -4 \end{cases}~\hfill A= \begin{cases} (-10~,~6)\\ (-10~,~-4) \end{cases}$