Question

Point B has coordinates ​(4,1​). The​ x-coordinate of point A is -8. The distance between point A and point B is 13 units. What are the possible coordinates of point​ A?

Answer 1

The possible coordinates of point A are (-8,-4) or (-8,6)

Explanation:

The distance between two points is given by the formula

`d = \sqrt{(x_(2)-x_(1))^(2) + (y_(2)-y_(1))^(2) }`

For point A
`(x_(1) , y_(1))`;
`x_(1)= -8` and
`y_(1)` is unknown

For point B
`(x_(2) , y_(2))`; (4,1) i.e
`x_(2)=4` and
`y_(2)=1`

and d = 13

Putting the values into the equation,

`13= \sqrt{[(4-(-8)]^(2) + (1-y_(1))^(2) }\\13= \sqrt{[(4+8)]^(2) + (1-y_(1))^(2) }\\13= \sqrt{12^(2) + (1-y_(1))^(2) }\\13^(2) = 12^(2) + (1-y_(1))^(2) \\169 = 144 +(1-y_(1))^(2)\\169-144 = (1-y_(1))^(2)\\25 = 1 -2y_(1) +y_(1)^(2) \\y_(1)^(2) -2y_(1)+1-25 =0\\y_(1)^(2) -2y_(1)-24 =0\\y_(1)^(2) -6y_(1) + 4y_(1) -24 =0 \\y_(1)(y_(1)-6) +4(y_(1) -6) = 0\\(y_(1)+4)(y_(1)-6) =0\\(y_(1)+4)=0 or (y_(1)-6) =0`

`y_(1)+4= 0` or
`y_(1)-6 =0`

`y_(1) =-4` or
`y_(1) = 6`

Hence, the possible coordinates of point A are (-8,-4) or (-8,6)