Question

The coordinates of A are (0,4) and the x-coordinate of B is 5. What is the y-coordinate of B if AB=13?(Two answers are possible.)
*could you give an explanation, i don't understand it but i know the possible answers which are 16 or -8*

Answer 1

$\overline{AB}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\\\ 13=\sqrt{(5-0)^2+(y_B-4)^2}\\ 13=\sqrt{25+y_B^2-8y_B+16}\\ 13=\sqrt{y_B^2-8y_B+41}\\ 169=y_B^2-8y_B+41\\ y_B^2-8y_B-128=0\\ y_B^2+8y_B-16y_B-128=0\\ y_B(y_B+8)-16(y_B+8)=0\\ (y_B-16)(y_B+8)=0\\ y_B=16 \vee y_B=-8$