Mathematics GE REVIEW Session 4

8/16/2019 Mathematics GE REVIEW Session 4

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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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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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EXAMPLE 3" The line passes throuh $)&%

/( and $x&1(+ #ind the !alue

a+ -' b+ ' c+ , d+ -1

Ans. A


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EXAMPLE 4" The line passes throuh

$)&%( & $0&-/( and $1)&.(+ #ithe !alue of .

a+ -', ',

c+ -),d+ ), Ans. C


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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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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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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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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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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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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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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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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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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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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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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 (x4,y4)

B (x,y)C (x@,y@)

Area = de!x@ y@ 1

x4 y4 1

x y 1

Formula:



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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



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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



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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



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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



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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

Mathematics GE REVIEW Session 4

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