Intersection of Loci You will be given a few conditions and asked to find the number of points that satisfy ALL the conditions simultaneously. The solution.

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Presentation transcript:

Intersection of Loci You will be given a few conditions and asked to find the number of points that satisfy ALL the conditions simultaneously. The solution is the point(s) where the LOCI INTERSECT. Remember, you want to know where the DASHED LINES intersect.

GivenLocus One Point Two Points One Line Two // Lines Two Intersecting Lines Circle Perpendicular Bisector 2 // lines on each side, same distance Third line // & in middle of given lines Angle Bisectors Summary of Locus Theorems

Linear Equations: Slanted lines y = mx + b y- y = m(x – x) Vertical lines x = ____ (no slope) Horizontal lines y = ____ (slope is 0) Slope Formula: Midpoint Formula: Circles: (a, b) is CENTER r = radius Parallel Lines: Same Slopes Perpendicular Lines: Negative Reciprocal Slopes

1. In the diagram below, town C lies on straight road p. Sketch the points that are 6 miles from town C. Then sketch the points that are 3 miles from road p. How many points satisfy both conditions? points

2. A city is planning to build a new park. The park must be equidistant from school A at (3,3) and school B at (3,-5). The park also must be exactly 5 miles from the center of town, which is located at the origin on the coordinate graph. Each unit on the graph represents 1 mile. On the set of axes below, sketch the compound loci and label with an X all possible locations for the new park. A B y = -1

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