Question

Find all possible values of x for which the distance between the points

A (x, -1) and B (5, 3) is 5 units.

Answer 1

We know that the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ ,

$d=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

Given d = 5 units and points are A (x, -1) and B (5, 3)

$\therefore \sqrt{(5-x{)}^2+(3--1{)}^2}=5$

$(5-x{)}^2+(3+1{)}^2=25$

$(5-x{)}^2+16=25$

$(5-x{)}^2=25-16$

$(5-x{)}^2=9$

$(5-x)=\sqrt{9}$

$(5-x)=\pm 3$

$x=5\pm 3$

$x=5+3or5-3$

$x=8or2$