Question

Find x if the distance between points A and B is 13 and point B is located in the second quadrant. A= (5, -1) B = (x, 4)

Answer 1

Given coordinates are

A(5,-1) and B(x,4).

The point B is in the second quadrant.

Now,

$\begin{gathered} AB=13 \\ \sqrt[]{(5-x)^2+(-1-4)^2}=13 \\ \sqrt[]{(5-x)^2+25}=13 \\ (5-x)^2+25=169 \\ (5-x)^2=144 \\ 5-x=\pm12 \\ x=17,-7 \end{gathered}$

Since the point B is in second quadrant, x can't be positive.

Therefore, the value of x is -7.