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?
Accepted Solution
A:
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 [tex]\sqrt{(1 - ( -8))^{2} + (2 - k)^{2}} = 15[/tex]
Now,squaring both sides, we get [tex](1 - ( -8))^{2} + (2 - k)^{2} = 225[/tex]
⇒ [tex](2 - k)^{2} = 225 - 9^{2} = 144[/tex]
⇒ 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 ([tex]x_{1}, y_{1}[/tex]) and ([tex]x_{2}, y_{2}[/tex]) is given by [tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex].