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8/16/2019 Mathematics GE REVIEW Session 4
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MATHEMATICSWith Casio fx 991-ES plus Calculator
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SESSION 4
Engr. Broddett B. Abatayo, GE, REA
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DISTANCE BETWEEN TWO POINTS
EXAMPLE 1" #ind the distance between $%&-
and $-)&-*(+
a+ 11+'1 b+ 9+*% c+ 1,+11 d+ +')
Ans. D
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DISTANCE BETWEEN TWO POINTS
EXAMPLE 2" If the distance between $'&.(
and $/&0( is 1'+ What is the !alue of .+
a+ ' b+ 19 c+ 1) d+ 11
Ans. B
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DISTANCE BETWEEN TWO POINTS
EXAMPLE 3" The line passes throuh $)&%
/( and $x&1(+ #ind the !alue
a+ -' b+ ' c+ , d+ -1
Ans. A
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DISTANCE BETWEEN TWO POINTS
EXAMPLE 4" The line passes throuh
$)&%( & $0&-/( and $1)&.(+ #ithe !alue of .
a+ -', ',
c+ -),d+ ), Ans. C
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DISTANCE BETWEEN TWO POINTS
EXAMPLE " Deterine the coordinates opoint which is '2* of the wa. fropoint $)&-*( and $-'&*(+
a+ $-1&1( b+ $-)&1( c+ $-1&)( d+ $1&-1(
Ans. A
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DISTANCE BETWEEN TWO POINTS
EXAMPLE !" The seent fro $-1&%( to $)extended three ties its owlenth+ The terinal point is
a+ $11&-)%( b+ $-11 c+ $11&-1/( d+ $11&
Ans. D
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DISTANCE BETWEEN TWO POINTS
EXAMPLE "" If $-)&-%( is the idpoint of $and $x&.(& then the !alues of. are
a+ x3) & .31 b+ x.3-1
c+ x31, & .3-1 d+ x.3-1
Ans. B
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DISTANCE BETWEEN TWO POINTS
EXAMPLE #" The line seent connectinand $9&.( is bisected b. the point #ind the !alues of x and .
a+ 1% & b+ '' & 1 c+ * & , d+ 1% &
Ans. C
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DISTANCE BETWEEN TWO POINTS
EXAMPLE $" #ind the coordinates of a poinequidistant fro $1&-(& $*&-( and $
a+ $)&-)( b+ $'&-)( c+ $'&-'( d+ $)&-'(
Ans. C
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DISTANCE BETWEEN A POINT AND A LIN
x
y
(x4,y4)
Ax + By + C = 0
d =√ A5 6 75
Ax4 + By4 + C
Formula:
d
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DISTANCE BETWEEN A POINT AND A LIN
EXAMPLE 1% " #ind the distance between *&0( and the line *x 8 . 6 9+
a+ 0+%' b+ 0+)9 c+ 0+/ d+ 0+*/
Ans. A
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DISTANCE BETWEEN A POINT AND A LIN
EXAMPLE 11" The distance between pointthe line *x 8 '. 6 ) is ,+/& #
location of a point+
a+ $%&'( b+ $-'&%(c+ $'&%( d+ $-%&'(
Ans. C
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DISTANCE BETWEEN A POINT AND A LIN
EXAMPLE 12" The distance between poin0( and the line is %+/*& #ind the
equation of a line+
a+ %x - *. 6 b+ %*. -
c+ %x - . 6 * d+ %. - *
Ans. D
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DISTANCE BETWEEN A POINT AND A LIN
EXAMPLE 13" The two points on the lines '. 6 % 3 , which are at a di
) fro the line'x 6 %. 8 3 , are
a+ $-*&1( and $-*&)( b+ $
and $%&-%( c+ $/&/( and $1)&1)( d+ $%and $-%&%(
Ans. B
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DISTANCE BETWEEN TWO PA&ALLEL
LINES
x
y
Ax + By + C4 = 0
Ax + By + C = 0
d
d =√ A5 6 75
C4 - C
Formula:
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DISTANCE BETWEEN TWO PA&ALLEL
LINES
EXAMPLE 14" #ind the distance between i!en lines
%x 8 '. 8 1) 3 , and %x 8 '3 ,+
a+ ' b+ %
c+ * d+ Ans. B
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DISTANCE BETWEEN TWO PA&ALLEL
LINES
EXAMPLE 1" #ind the distance betweenlines
'x 6 . 8 1) 3 , and 'x 6 ,+
a+ )+'1 b+
c+ '+'' d+
Ans. B
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SLOPE O' A LINE
(x4,y4)
(x,y)
x
y
m =y - y4
x - x4
: x
y
m = - A
7Where: x ; x4
Y = A + Bx
x
y
m = B
Give !"o #oi!$:
Give $lo#e-i!er%e#! &orm e'ua!io o& a lie:
Give eeral e'ua!io o& a lie:
Give !he ale o& i%lia!io
m = !a :
Ax + By + C = 0
x
y
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SLOPE O' A LINE
EXAMPLE 1!" #ind the slope of a line de<b. . 8 x 3 *
a+ 1 b+ 12%
c+ -12) d+ 12)Ans. A
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SLOPE O' A LINE
EXAMPLE 1"" What is the slope of the line6 ). 6 1 3 ,
a+ '2) b+ )
c+ -'2) d+ -Ans. C
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SLOPE O' A LINE
EXAMPLE 1#" A line passes trouh $1&*( a$1,&-/(+ #ind the slope of the
a+ -*2 b+ -1' c+ -12) d+ '2)
Ans. B
SLOPE O' A LINE
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SLOPE O' A LINE
EXAMPLE 1$" The slope of the line =oininpoints $'&-*( and $%&1,( is
a+ 1* b+ -1*
c+ 1) d+ 11
Ans. A
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X AND ( INTE&CEPT
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X AND ( INTE&CEPT
EXAMPLE 21" #ro the i!en points $1&*($1,&-/(+ #ind the x-intercept
a+ */20 b+ * c+ */211 d+ */
Ans. B
X AND ( INTE&CEPT
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X AND ( INTE&CEPT
EXAMPLE 22" #ro the i!en points $1&*( $1,&-/(+ #ind the .-intercept
a+ */20 b+ */ c+ */211 d+ */2
Ans. D
A&EA )I*EN THE *E&TICES
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A&EA )I*EN THE *E&TICES
!
A (x4,y4)
B (x,y)C (x@,y@)
Area = de!x@ y@ 1
x4 y4 1
x y 1
Formula:
A&EA )I*EN THE *E&TICES
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A&EA )I*EN THE *E&TICES
EXAMPLE 23" i!en the !ertices of a trianwhose coordinates are $
$'&-'( and $*&-'(+ #ind the area of trianle
a+ ' sq+ units b+
units c+ * sq+ units d+ units
Ans. B
A&EA )I*EN THE *E&TICES
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A&EA )I*EN THE *E&TICES
EXAMPLE 24" i!en the !ertices of a trianwhose coordinates are $-
$%&,( and $'&'(+ #ind the area of ttrianle
a+ / sq+ units b+ 9 s
units c+ 1, sq+ units d+11 units
Ans. B
A&EA )I*EN THE *E&TICES
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A&EA )I*EN THE *E&TICES
EXAMPLE 2" i!en the !ertices of a squawhose coordinates are $1
$,&/( & $%&*( and $-'&%(+ Whathe area
a+ ), sq+ units b+ ',
units c+ )* sq+ units d+'* sunits
Ans. C
E+,ATION O' A LINE
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E+,ATION O' A LINE
y = mx + b (*lo#e-!er%e#! 'ua!io o& a ie)
y – y 1 = m( x – x
1) (.oi!-*lo#e 'ua!io o& a ie)
Ax + By + C = 0 (Geeral Form &or !he 'ua!io o& a ie)
x = a (/orio!al ie 'ua!io)
y = b (1er!i%al ie 'ua!io)
x/a + y/b = 1 (2"o !er%e#! Form &or !he 'ua!io o& a ie)
E+,ATION O' A LINE
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E+,ATION O' A LINE
EXAMPLE 2!" #ind the equation of a line pthrouh the oriin and with a slop
a+ . 8 x 3 , b+ .c+ . 6 x 3 - d+
3 ,Ans. A
E+,ATION O' A LINE
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E+,ATION O' A LINE
EXAMPLE 2"" A line passes trouh $1&-'( a%&)(+ Write the
equation of the line in slopintercept for
a+ . 8 % 3 x b+
- ) c+ . 3 x - % d+ 3 x
Ans. B
E+,ATION O' A LINE
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E+,ATION O' A LINE
EXAMPLE 2#" The equation of a line thatintercepts the x-axis at x3% and
axis at .3- is
a+ 'x 6 ). 3 1) b+ 3 1)
c+ 'x - ). 3 1) d+ )'. 3 1)
Ans. C
E+,ATION O' A LINE
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E+,ATION O' A LINE
EXAMPLE 2$" #ind the equation of a linethrouh point $'&1( and is
perpendicular to the line x 6 *. 6* 3 ,+
a+ *x - ). 3 1% b+ *3 1%
c+ )x - *. 3 1% d+ *. 3 1%
Ans. B
E+,ATION O' A LINE
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E+,ATION O' A LINE
EXAMPLE 3%" What is the equation of the passin throuh $-)&( wi
x-intercept half the .- intercep
a+ x - . 3 b+ )). 6 ) 3 ,
c+ 'x 6 . 8 ) 3 , d+ )8 ) 3 , Ans. D
E+,ATION O' A LINE
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E+,ATION O' A LINE
EXAMPLE 31" A line passes throuh $)&)(the equation of the line if the len
the line seent intercepted b. thcoordinates axes is the square *+
a+ )x 6 . -) 3 , b+ )) 3 , c+ )x - . 6 ) 3 , d+ )6 ) 3 ,
Ans. B
AN)LE BETWEEN THE TWO LINES
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x
y
:
4
Formula:
!a =: - 4
1 6 4
AN)LE BETWEEN TWO LINES
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EXAMPLE 32" A line passes throuh $1&*( $1,&-/(+ #ind the anle it a?es w
x-axis+
a+ *+'*%*B b+*'+'%%/B
c+ -**+',%/B d+-*%+%%B
Ans. C
AN)LE BETWEEN TWO LINES
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EXAMPLE 33" #ind the acute anle ofintersection of the lines 'x - 0.
and )x 6 *. 3 1+
a+ *,B b+ %*B c+ -',B d+ -%,
Ans. B
AN)LE BETWEEN TWO LINES
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EXAMPLE 34" A line with an inclination of passes throuh
$-*2)&-92)(+ What is the x-coof a point on the line if itscorrespondin .-coordinate is
a+ b+ 0 c+ / d+ 9Ans. C