Question

Point B has coordinates (5,2). The x-coordinate of point Ais - 1. The distance between point A and

point B is 10 units. What are the possible coordinates of point A?
The possible coordinates of point A are 1
(Type an ordered pair. Use a comma to separate answers as needed.)

Answer 1

`\large \boxed{(-1,-6),(-1,10)}`

Explanation:

Point A must be on a circle with centre at (5,2) and radius 10.

The centre-radius form for the equation of a circle is

(x – h)² + (y – k)² = r², where

(h,k) = the coordinates of the centre and

r = the radius

Thus, the equation for this circle is

(x - 5)² + ( y - 2)² = 10²

Substitute the value for x and solve for y:

`\begin{array}{rcl}\\(x - 5)^(2) +( y - 2)^(2) &=& 10^(2)\\(-1 - 5)^(2) +( y - 2)^(2) &=& 100\\(-6)^(2) +( y - 2)^(2) &=& 100\\36 +( y - 2)^(2) &=& 100\\( y - 2)^(2) &=& 64\\y - 2 = -8 & \qquad & y - 2 = 8\\y = \mathbf{-6} & \qquad & y = \mathbf{10}\\\end{array}\\\text{The possible coordinates of A are $\large \boxed{\mathbf{(-1,-6),(-1,10)}}$}`

The figure below shows the circle intersecting the line x = -1 at (-1,-6) and (-1,10).