Question

Point B has coordinates ​(2​,1​). The​ x-coordinate of point A is negative 7. The distance between point A and point B is 15 units. What are the possible coordinates of point​ A?

Answer 1

(-7,-11) or (-7,13)

Explanation:

Let us assume that the possible coordinates of point A are (-7,k).

Now, the distance between point B(2,1) and point A(-7,k) is 15 units.

So, we can write
`\sqrt{(-7-2)^(2)+(k-1)^(2)  } = 15`

Now, squaring both sides we get

`(-7-2)^(2)+(k-1)^(2) = 225`

⇒ 81 + (k - 1)² = 225

⇒ (k - 1)² = 144

⇒ k - 1 = ± 12

⇒ k = - 11 and k = 13

Therefore, the possible coordinates of point A are (-7,-11) or (-7,13). (Answer)