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Analytic
Geometry
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SPECIFIC OBJECTIVES:
At the end of the lesson, the student isexpected to be able
to:
Familiarize with the use of CartesianCoordinate System.
etermine the distance between two points.
e!ne and determine the an"le of inclinationsand slopes of a
sin"le line, parallel lines,perpendicular lines and intersectin"
lines.
etermine the coordinates of a point ofdi#ision of a line
se"ment.
e!ne the median of the trian"le and !nd theintersection point of
the medians of the trian"le.
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F$%A&'%(A) C*%C'+(S
'F%(*%S
Analytic Geometry - is the branch ofmathematics, which deals
with the properties,
beha#iors, and solution of points, lines, cur#es,an"les,
surfaces and solids by means of
al"ebraic methods in relation to a coordinatesystem.
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Two Parts of Analytic Geometry. +lane Analytic Geometry - deals
with
!"ures on a plane surface/. Solid Analytic Geometry - deals
with
solid !"ures
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Directed Line- a line in which one
direction is chosen as positi#e and the oppositedirection as
ne"ati#e.
Directed Line Segment - consistin" ofany two points and the part
between them.
Directed Distance - the distancebetween two points either
positi#e or ne"ati#e
dependin" upon the direction of the line.
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RECTANG!AR COOR"INATES
A pair of number 0x, y1 in which x is the!rst and y bein" the
second number is
called an ordered pair.
A #ertical line and a horizontal linemeetin" at an ori"in, *,
are drawn which
determines the coordinate axes.
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Coordinate Plane - is a plane
determined by the coordinate axes.
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X axis - is usually drawn horizontallyand is called as the
horizontal axis.Y axis - is drawn #ertically and is
called as the #ertical axis.
O- the ori"inCoordinate- a number corresponds to
a point in the axis, which is de!ned in
terms of the perpendicular distance fromthe axes to the
point.
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"ISTANCE BET#EEN
T#O POINTS
$% &ori'ontal
(he len"th of a horizontal line se"ment isthe abscissa 0x
coordinate1 of the point onthe ri"ht minus the abscissa 0x
coordinate1 of the point on the left.
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(% Vertical
(he len"th of a #ertical line
se"ment is the ordinate 0ycoordinate1 of the upper pointminus
the ordinate 0y coordinate1of the lower point.
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)% Slant
(o determine the distancebetween two points of a slant line
se"ment add the s2uare of thedi3erence of the abscissa to
thes2uare of the di3erence of theordinates and ta4e the
positi#es2uare root of the sum.
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SA*P!E PROB!E*S
5. Show that the trian"le A 0, 51, 6 07, 81 and C
0/, /1 is a ri"ht trian"le.
9.9. (he #ertices of the base of an isoscelestrian"le are 0, /1
and 05, 1. Find theordinate of the third #ertex if its abscissa is
8.
8.Find the radius of a circle with center at 05, 1,if a chord of
len"th 5 is bisected at 0;, 51.
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9. Find the distance between the points 05, /1and 08, 91.
8. 6y addition of line se"ments show whetherthe points A0
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SA*P!E PROB!E*S
. etermine the distance between
a. 0/,
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9. Find the distance between the points 05, /1
and 08, 91.
8. 6y addition of line se"ments show whetherthe points A0
