Question

Point B has coordinates ​(4,1). The​ x-coordinate of point A is -4. The distance between point A and point B is 10 units. What are the possible coordinates of point​ A?

Answer 1

Given:

Point B has coordinates ​(4,1).

The​ x-coordinate of point A is -4.

The distance between point A and point B is 10 units.

To find:

The possible coordinates of point​ A.

Solution:

Let the y-coordinate of point A be y. Then the two points are A(-4,y) and B(4,1).

Distance formula:

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

The distance between point A and point B is 10 units.

$\sqrt{(4-(-4))^2+(1-y)^2}=10$

Taking square on both sides, we get

$(8)^2+(1-y)^2=100$

$(1-y)^2=100-64$

$(1-y)^2=36$

Taking square root on both sides, we get

$(1-y)=\pm \sqrt{36}$

$-y=\pm 6-1$

$y=1\mp 6$

$y=1-6$ and $y=1+6$

$y=-5$ and $y=7$

Therefore, the possible coordinates of point​ A are either (-4,-5) or (-4,7).