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Unformatted text preview: 10.7 Locus 10.7
p. 642 Locus Locus
Definition: the set of all points in a Definition: plane that satisfy a given condition or a set of given conditions. or Plural – Loci Pronounced: “low-sigh” Ex: what is the locus of points that the end of the second hand on a clock forms? on
A circle Ex: Draw a line k on a piece of Ex Draw paper. Draw & describe the locus of points on the paper that are 1 cm from the line k. from
k 1 cm m
1 cm n 2 lines, m & n, to lines, line k and 1 cm away on either side. on 4 steps to finding a locus steps
1. 2. 3. 4. Draw any figures that are given. Locate several pts that satisfy the Locate condition. condition. Continue until a pattern is Continue recognized. recognized. Draw the locus & describe it in Draw words. words. Finding locus for 2 or more conditions Finding Find the locus for each individual Find condition 1st. condition Then, find the intersection of the Then, conditions. conditions. This intersection is the solution. Ex: Given ΔABC, what is the locus ABC, of points that are =dist from AB & AC and also =dist from A & B? AC =dist
∠ bisector of ∠ A
A Intersection of the 2 Intersection lines is the solution. lines
B C ⊥ bisector of AB bisector Ex: What is the locus of pts 2 cm Ex What from X & 3 cm from Y? from
If XY > 5, locus is 0 pts.
X 2 3 Y If XY = 5, locus is 1 pt. If XY < 5, locus is 2 pts. X 2 3 Y X 2 Y 3 Definitions Definitions
Epicenter – the pt. on the surface of the earth Epicenter directly above an earthquake’s origin. directly Seismograph – tool that measures distance to Seismograph the epicenter, but not the direction to the epicenter. epicenter. To locate an epicenter, 3 locations for To seismographs are needed. seismographs The place where all 3 circles intersect is the The epicenter. epicenter. Ex: 3 readings from seismographs are as Ex readings follows: at A(2,4) – epicenter is 2 miles away, at B(2,-.5) – epicenter is 2.5 miles away, & at C(-1,2) – epicenter is 3 miles away. Where is the epicenter? the A C (2,2) B Assignment Assignment ...
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- Spring '11