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=√((x_2-x_1)^2+(y_2-y_1)^2)`

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

`√((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 √(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).