Question

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

A (2, -3) and B (10, y) is 10 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 = 10 units and points are A (2, -3) and B (10, y)

$\therefore \sqrt{(10-2{)}^2+(y--3{)}^2}=10$

$8^2+(y+3{)}^2=100$

$(y+3{)}^2+64=100$

$(y+3{)}^2=100-64$

$(y+3{)}^2=36$

$(y+3)=\sqrt{36}$

$(y+3)=\pm 6$

$y=\pm 6-3$

$y=6-3or-6-3$

$y=3or-9$