tugas 3 geo analitik bidang dan ruang

7/29/2019 Tugas 3 Geo Analitik Bidang Dan Ruang

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Tugas 3 Geometri Analitik Bangun Dan Ruang

BY : USMCR010 Page 1

NAMA : PHELIPUS MERE

NIM : 1001036019

PRODI : P. MIPA

SEMESTER : V

1. Find the signet distance between the given line and point, determinewhether the point is above or below the line.5x + 12y 31 = 0, (6,1)Answer:

d =

=( ) ( )

=

=

2. a. Find the equation of the line that contains the point (17,12) and isperpendicular tothe line 5x + 12y 60 = 0

b. Find the point of intersection of these linesc. Find the distance between this point of intersection and given pointd. Check the result of ( c ) by using (4).Answer:a. 5x + 12y 60 = 0

y = + 5 => = , =

y y1 = m(x x1)

y 12 = ( 17)

y = +

y = =>

b. =

144x 1728 = -25x + 300, x = 12

5x + 12y 60 = 0, y =

x = 5y = 12x 144

x =

=

144y + 720 = 25y + 720169y = 0y = 0, so the point intersection is (12,0)

c. = (12 17) + (0 12) = 169 = 13

d. =( ) ( )

= = 13


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3. Find the perpendicular distane between the given pair of parallel lines4x 3y 15 = 0, 4x 3y + 15 = 0Answer:

We get one point which passed by L1 to find the distance between L1and L2, so we get (5,0)Because B cant b < 0, we multiplying the equation of L2 whith (-1). -4x + 3y 15 = 0

d =( ) ( )

= = 7

4. Find the equation of theline that bisect the angle from the line 3x + 4y 10 = 0 to the line 5x 12y + 2 = 0Answer:

From the figure, we have d1 = -d2

=

=

=-5(5x -12y + 2) = (3x 4y + 10) 13


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-25x + 60y 10 = -39x 52y + 1307x + 4y 60 =0

5. Find the equation of theline that bisect the acute angles formed by the

lines 7x 24y + 40 = 0 and 3x + 4y 8 = 0Answer:

From the figure, we have d1 = d2

=

=

=5( -7x + 24y 40) = ( 3x + 4y 8)-25-35x + 120y 200 = -75x 100y + 2002x + 11y 20 = 0

Soal diatas diambil dari buku PLANE ANALYTIC GEOMETRY halaman 45no 2, 7, 9, 14 dan 15 sebagai no 1 s/d 5 dalam posting saya.

tugas 3 geo analitik bidang dan ruang

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