LESSON 42 Finding Distance from a Point to a Line REVIEW FIND AD, AC, AND AB TO THE NEAREST TENTH THEOREM 42-1 Through a line and a point not on a line, there exists exactly one perpendicular line to the given line. Line p is the only line through point U that is perpendicular to line n THEOREM 42-2 FIND THE DISTANCE FROM POINT A TO THE LINE THEOREM 42-3 The perpendicular segment from a point to a plane is the shortest segment from the point to the plane. Therefore, AB is the shortest distance to plane WVX THEOREM 42-4 If two lines are parallel, then all points on one line are equidistant from the other line. APPLICATION IN CONSTRUCTION Marty wants to hang ceiling tile in his game room. He wants each row of his tracks to be parallel to the first row. He measures the distance between the 1 st & 2 nd rows to verify they are parallel. However, his measure tape is not long enough to reach across the room. How can he ensure all rows are parallel to the 1 st row? Using Transitive Property of Parallel Lines he needs to make each row parallel to the previous row. Why do the measurements between the rows verify they were parallel? Theorem 42-4 states if the rows are parallel, then those measurements should be the same anywhere on the them. APPLICATION IN MAPS IN CONCLUSION Using Geometry, where on the free throw line should you stand when attempting a shot? Why? At the midpoint It will be the shortest distance to the basket Thm 42-2
