Show all work please Find all the points having an xcoordina

Show all work please.

Find all the points having an x-coordinate of 9 whose distance from the point (3, -2) is 10. (9, -12), (9, 8) (9, 6), (9, -10) (9, 13), (9, -7) (9, 2), (9, -4)

Solution

let the y coordinate of that point be y.

as distance between (9,y) and (3,-2) is 10

sqrt((3-9)^2 +(y-(-2))^2))=10

squaring both sides

6^2 +(y+2)^2 =100

(y +2)^2 =64

square rooting both sides

y+2 =8,y+2 =-8

y =6,y =-10

so the points are (9,6) and (9,-10)

correct option is 2.

Thank you