Today we took a quiz on sections 3-1 to 3-4. After the quiz, we corrected the homework from last night. There were a lot of questions regarding the steps, so I modeled a couple of hw problems and allowed an extra day to redo (or do) the hw.
We did not have time to begin the lesson on spherical geometry. It will happen tomorrow.
It took longer than I expected to teach the distance between a point and a line because some of you needed a review on graphing linear equations, the distance formula, and the slopes of perpendicular lines.
Remember that given a line and a point (the point not on the given line), we can construct the line perpendicular to the given line from the point. We do this by starting at the given point and moving according to the slope of the perpendicular. This slope of the perpendicular is known because it is the opposite reciprocal of the slope of the given line. The slope of the given line is in its equation! So, now connect the given point to the point the slope takes you to, and label its coordinates. The problems in the book are nice such that these points keep landing on the original line. Now find the length of the segment just drawn. It is the segment perpendicular to the line from the point. This is how you find the distance between a point and a line.
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