Question

The distance between A(1, 3) and B(x, 7) is 5. Calculate the possible values of x

Answer 1

$A(1,3)$, $B(x,7)$

$AB=5$ units

Distance between two points $=\sqrt{(x_1-x_2{)}^2+(y_1-y_2{)}^2}$

$(x_1,y_1)$ and $(x_2,y_2)$

$AB=\sqrt{(x-1{)}^2+(7-3{)}^2}$

Squaring Both sides

$(AB{)}^2=(x-1{)}^2+(4{)}^2$

$(5{)}^2=x^2-2x+1+16$

$25=x^2-2x+17$

$x^2-2x-8=0$

$x^2-4x+2x-8=0$

$(x-4)(x+2)$

$x=-2$ or $4$