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

The possible coordinates of point A are (-8, 14) and (-8, -10).

Step-by-step explanation:

To find the possible coordinates of point A, we need to consider that the x-coordinate of point A is -8 and the distance between point A and point B is 15 units. Since point B has coordinates (1, 2), we can use the distance formula to find the y-coordinate of point A.

The distance formula is given by:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the known values,
15 = sqrt((1 - (-8))^2 + (y2 - 2)^2)

Simplifying the equation,
15 = sqrt(81 + (y2 - 2)^2)

Squaring both sides, we get:
225 = 81 + (y2 - 2)^2

Subtracting 81 from both sides, we have:
144 = (y2 - 2)^2

Taking the square root of both sides, we get:
12 = |y2 - 2|

Splitting the equation into two cases,
Case 1: y2 - 2 = 12, which gives y2 = 14
Case 2: -(y2 - 2) = 12, which gives y2 = -10

Therefore, the possible coordinates for point A are (-8, 14) and (-8, -10).

Answer 2

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)}`.