Question

Point B has coordinates ​(1​,2​). The​ x-coordinate of point A is negative 8. The distance between point A and point B is 15 units. What are the possible coordinates of point​ A?

Answer 1

Answer:

The point A will be  (-8,14) or (-8,-10).

Step-by-step explanation:

Point B has coordinates (1,2) and the x-coordinate of point A is - 8.

Let us assume that the coordinates of point A are (-8,k).

Now, given that the point A is 15 units apart from point B.

Therefore, from the distance formula, we can write that  

$\sqrt{(1 - ( -8))^{2} + (2 - k)^{2}} = 15$

Now,squaring both sides, we get  

$(1 - ( -8))^{2} + (2 - k)^{2} = 225$

⇒ $(2 - k)^{2} = 225 - 9^{2} = 144$

⇒ 2 - k = ± 12

⇒ k = 14 or -10.

Therefore, the point A will be  (-8,14) or (-8,-10). (Answer)

We know that the distance between two points on the coordinate plane ($x_{1}, y_{1}$) and ($x_{2}, y_{2}$) is given by  

$\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$.