Geometry: An Interactive Journey to Mastery

Solution
The segment PQ has slope^0741  ^73 , so the perpendicular bisector to PQ has slope^37.
It also passes through the midpoint of PQ, which is §· ̈ ̧©¹^5722 ,.
The equation of the perpendicular bisector is thus yx 73 5 27 §· ̈ ̧©¹ 2.
Study Tip
x As Example 4 shows, there is no need to be perturbed by awkward numbers. Work to simply
understand, and hold on to the basic theory behind the equations of lines.
Pitfall
x Many students are locked into the y = mx + b formula for straight lines. It is rare that this is the easiest
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a line.

1. Find the slopes of the lines passing through each of the following pairs of points.
   D௘ͽ ͼ௘௘ͽDQGͼ௘௘ͽ
   E௘ͽ ͼ௘í௘ͽDQGͼ௘íí௘ͽ
   F௘ͽ ͼ௘௘ͽDQGͼ௘a, b௘ͽ
   G௘ͽ ͼ௘a, a௘ͽDQGͼ௘a + b, a + b௘ͽ
   H௘ͽ ͼ௘a௘ͽDQGͼ௘b, c௘ͽ
   I௘ͽ ͼ௘a, b௘ͽDQGͼ௘íb, a௘ͽ
   J௘ͽ ͼ௘a௘ͽDQGͼ௘a௘ͽ

Problems