tugas 3 geo analitik bidang dan ruang
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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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Tugas 3 Geometri Analitik Bangun Dan Ruang
BY : USMCR010 Page 2
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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Tugas 3 Geometri Analitik Bangun Dan Ruang
BY : USMCR010 Page 3
-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.
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