JL¯¯¯¯¯¯¯ is a perpendicular bisector of KM¯¯¯¯¯¯¯¯¯¯ . Hallie locates point H along line segment JL¯¯¯¯¯¯¯. If the length of KH¯¯¯¯¯¯¯¯¯ is given by 6y+3 and the length of HM¯¯¯¯¯¯¯¯¯¯ is given by 2y+7, what is the length in units of segment HM¯¯¯¯¯¯¯¯¯¯? (1 point) Responses 8 8 1 1 9 9 18
Since JL is a perpendicular bisector of KM, this means that KH and HM are congruent. So, we have that 6y+3 = 2y+7 (since KH is equal to HM). Subtract 2y from both sides of the equation to get 4y+3 = 7. Subtract 3 from both sides of the equation to get 4y = 4. Divide both sides of the equation by 4 to get y = 1.
So the length of HM is 2y+7 = 2(1)+7 = 2+7 = 9 units.