Please help!
Jason's gf lives in a house on Clifton Highway which has equation y=8, The distance 'as the crow flies' from Jason's house to his gf's house is 11.73 km. If Jason lives at (4,1), what are the coordinates of his gf's house?

I am so confused, because I made a line for the highway with y=8 and a point below J(4,1), but I'm not sure how to work it out... Jasons gf's house should be at (x,8), but I am not sure.,.

Question

Please help!
Jason's gf lives in a house on Clifton Highway which has equation y=8, The distance 'as the crow flies' from Jason's house to his gf's house is 11.73 km. If Jason lives at (4,1), what are the coordinates of his gf's house?

I am so confused, because I made a line for the highway with y=8 and a point below J(4,1), but I'm not sure how to work it out... Jasons gf's house should be at (x,8), but I am not sure.,.

cherylim23 · Answer

Just use distance formula:
Let gf be G(x,8)
D = sqrt (J^2 + G^2) = sqrt ( (4-x)^2 +(1-8)^2 )
11.73 = sqrt( x^2 - 8x + 16 +(-7)^2 )
11.73^2 = x^2 - 8x + 16 + 49
Solve that and you should get x = 13.41238 or x = -5.41238
Both are valid answers