7/27/2019 Tugas 1 Goe Analitik

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Tugas 1 Geometri Analitik Bangun Dan Ruang

BY : USMCR010 Page 1

NAMA : PHELIPUS MERE

NIM : 1001036019

PRODI : P. MIPA

SEMESTER : V

1. By the use of components show that the points P1(-2,5), P2(3,9),P3(11,7) and P4(6,3) are the vertices of a parallelogram.

2. Given the points P1(-5,-2), P2(1,4), P3(3,1), P4(8,4) and P5(1,-2), showthat the algebraic sum of the components of the segments P1P2, P2P3,P3P4, and P4P5 on either coordinate axis is the component of the

closing segment P1P5 on this axis.Answer:Dik: P1 = (-5,-2), P2 = (1,4), P3 = (3,1), P4 = (8,1), P5 =(1,-2) P1P2 = P2 P1

For x = P2 P1 = 1-(-5) = 6For y = P2 P1 = 4 (-2)= 6, so x,y = (6,6)

P2P3 = P3 P2For x = P3 P2 = 3 1 = 2For y = P3 P2 = 1 4 = -3, so x,y = (2,-3)

P3P4 = P4 P3For x = P4 P3 = 8 3 = 5For y = P4 P3 = 1 1 = 0, so x,y = (5,0)

P4P5 = P5 P4For x = P5 P4 = 1 8 = -7For y = P5 P4 = -2 1 = -3, so x,y = (-7,-3)

Sum point x = 6 + 2 + 5 + -7 = 6Sum point y = 6 + (-3) + 0 + (-3) = 0So x,y = (6,0) P1P5 = P5 P1

For x = P5 P1 = 1 - (-5) = 6For y = P5 P1 = -2 (-2) = 0, so x,y = (6,0)

So, sum points P1P2, P2P3, P3P4, P4P5 = P1P5

7/27/2019 Tugas 1 Goe Analitik

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Tugas 1 Geometri Analitik Bangun Dan Ruang

BY : USMCR010 Page 2

3. For the points of problem 4 show that the sum of the components ofthe segments P1P2, P2P3, P3P4, P3P4, and P5P1 on either coordinateraxis is zero.Answer:Seperti pada hasil no 2 bahwa

Jumlah P1P2, P2P3, P3P4, P3P4 have coordinat (6,0)P5P1 = (6,0)Distance between : P5P1 - P1P2, P2P3, P3P4, P3P4For x = 6 6 = 0For y = 0 0 = 0, so x,y = (0,0)

4. The points P1(-2,1), P2(1,2), P3(7,4) lie on the same straight line. Byuse of components find the ratio of P1P2 to P2P3.Answer:Dik: P1 = (-2,1), P2 = (1,2), P3 = (7,4)

P1P2 = P2 P1For x = 1 (-2) = 3For y = 2 1 = 1, so x,y = (3,1)

P2P3 = P3 P2For x = 7 1 = 6For y = 4 2 = 2, so x,y = (6,2)

P1P2 : P2P3For x = 3 : 6 = 1: 2For y = 1 : 2, so P1P2 : P2P3 = 1 : 2

Soal diatas diambil dari buku PLANE ANALYTIC GEOMETRY halaman 6

no 3, 4, 5, dan 7 yang saya posting sebagai no 1, 2, 3 dan 4.

Us mcr 010