Geometry 10.7 Locus not Locust!.

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Presentation transcript:

Geometry 10.7 Locus not Locust!

Goals Know what Locus is. Find the locus given several conditions. January 12, 2019 Geometry 10.7 Locus

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. January 12, 2019 Geometry 10.7 Locus

Locus Example 1 What is the locus of points on a plane equidistant from a given point? A circle. January 12, 2019 Geometry 10.7 Locus

Locus Example 1 What is the locus of points on a plane equidistant from a given point? A circle. January 12, 2019 Geometry 10.7 Locus

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. January 12, 2019 Geometry 10.7 Locus

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. January 12, 2019 Geometry 10.7 Locus

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. January 12, 2019 Geometry 10.7 Locus

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. January 12, 2019 Geometry 10.7 Locus

Locus problems are not difficult, but require thought. January 12, 2019 Geometry 10.7 Locus

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 January 12, 2019 Geometry 10.7 Locus

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. January 12, 2019 Geometry 10.7 Locus

Problem 1 Solution The locus is a circle that is internally tangent to the given circle and with half of the diameter. January 12, 2019 Geometry 10.7 Locus

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. January 12, 2019 Geometry 10.7 Locus

Problem 2 Solution Area Square: 2 3  3 = 9 Rectangles: 2 3 4(2  3) = 24 Circle:   22 = 4 Total = 9 + 24 + 4  45.57 2 2 3 3 2 January 12, 2019 Geometry 10.7 Locus

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. January 12, 2019 Geometry 10.7 Locus

Problem 3 Solution The perpendicular bisector of the segment between the centers of the two given circles. January 12, 2019 Geometry 10.7 Locus

You cannot do locus problems without THINKING. January 12, 2019 Geometry 10.7 Locus