Geometry 10.7 Locus not Locust!. June 8, 2015Geometry 10.7 Locus2 Goals  Know what Locus is.  Find the locus given several conditions.

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Presentation transcript:

Geometry 10.7 Locus not Locust!

June 8, 2015Geometry 10.7 Locus2 Goals  Know what Locus is.  Find the locus given several conditions.

June 8, 2015Geometry 10.7 Locus3 What is a LOCUS?  A set of points that satisfy some given condition.  Root is the Latin word for “Location”.  Plural of Locus is Loci (low-sigh).  Thinking of locus as a path may help.

June 8, 2015Geometry 10.7 Locus4 Locus Example 1  What is the locus of points on a plane equidistant from a given point? A circle.

June 8, 2015Geometry 10.7 Locus5 Locus Example 1  What is the locus of points on a plane equidistant from a given point? A circle.

June 8, 2015Geometry 10.7 Locus6 Locus Example 2  What is the locus of points equidistant from two given points? How do we describe this line? It’s the perpendicular bisector of the segment between the two points.

June 8, 2015Geometry 10.7 Locus7 Locus Example 3 – you try it.  What is the locus of points on a plane equidistant from line L? L How would you describe this? Two lines parallel to L, one on each side.

June 8, 2015Geometry 10.7 Locus8 Locus Example 4 – you do it.  What is the locus of points equidistant from two perpendicular lines? Description? Two perpendicular lines that are the angle bisectors of the original lines.

June 8, 2015Geometry 10.7 Locus9 How to Determine a Locus  Locate a number of points which satisfy the given condition(s).  Draw a line (or curve) through these points.  Describe accurately the figure you have drawn.

June 8, 2015Geometry 10.7 Locus10

June 8, 2015Geometry 10.7 Locus11 Problems to solve.  Do not talk about it.  Do not ask questions.  Think!  Try to visualize in your “minds-eye”.  Doodle or sketch if it helps.  Write down a precise, accurate description

June 8, 2015Geometry 10.7 Locus12 Problem 1  Find the locus of the midpoints of all chords that can be drawn from a fixed point in the circumference of a circle.

June 8, 2015Geometry 10.7 Locus13 Problem 1 Solution The locus is a circle that is internally tangent to the given circle and with half of the diameter.

June 8, 2015Geometry 10.7 Locus14 Problem 2  A point moves so that it is always outside a square 3 ft. on a side and so that it is always 2 ft. from the nearest point of the square. Find the area enclosed by the locus of this moving point.

June 8, 2015Geometry 10.7 Locus15 Problem 2 Solution Area Square: 3  3 = 9 Rectangles: 4(2  3) = 24 Circle:   2 2 = 4  Total =   45.57

June 8, 2015Geometry 10.7 Locus16 Problem 3  Find the locus of the center of a circle which is externally tangent to each of two given non-intersecting and congruent circles.

June 8, 2015Geometry 10.7 Locus17 Problem 3 Solution The perpendicular bisector of the segment between the centers of the two given circles.

June 8, 2015Geometry 10.7 Locus18 You cannot do locus problems without THINKING.