Question

Line s is the perpendicular bisector of JK. If line s intersects JK at point L, which of the following statements must be true? Check all that apply.

a) PE⊥EX
b) PE∥EX
c) both a and b
d) none of the above

Answer 1

Option (d) none of the above is correct, because there is no information about lines PE and EX in relation to the perpendicular bisector line s of JK; thus, we cannot confirm any of the relationships mentioned in options (a) or (b).

Step-by-step explanation:

If line s is the perpendicular bisector of JK, it means that point L is the midpoint of JK and line s is perpendicular to JK at point L. Therefore, the statements that must be true are those related to perpendicularity and bisecting. In this scenario, we're not provided with sufficient information about the lines PE and EX, so we cannot deduce their relationship based solely on the information given about line s and JK.

Since line s is a perpendicular bisector, it will intersect JK at a 90° angle, and JL will equal LK in length because a bisector divides a line into two equal parts. None of the statements given as options (a, b, c, d) specify the relationship between PE and EX to line s or JK. Thus, the correct statement must be (d) none of the above, as nothing is mentioned about PE and EX in the context of line s bisecting JK at L.