Question

Persamaan garis yang melalui titik T (-3,-4) dan tegak lurus dengan garis yang melalui titik (2,-2) dan (-2-8) adalah...

Answer 1

Persamaan garis :

y - y1 = x - x1
y2-y1    x2-x1

y - (-2) = x - 2
-8- (-2)    -2-2

y + 2 = x - 2
  -6         -4

-4y - 8 = -6x + 12
-4y = -6x + 12 + 8
-4y = -6x + 20
4y = 6x - 20
y = 6/4x - 5
y = 3/2x - 5

y = mx + c
m = 3/2

karena tegak lurus :

m1 . m2 = -1
3/2 . m2 = -1
m2 = -1 / (3/2)
m2 = -2/3

y - b = m (x - a)
y - (-4) = -2/3(x -(-3))
y + 4 = -2/3(x + 3)
y + 4 = -2/3x - 2
y = -2/3x - 2 - 4
y = -2/3x - 6
kalikan 3

3y = -2x - 18

atau

3y + 2x + 18 = 0

atau

3y + 2x = -18

Answer 2

M1 = -2 - (-8) / 2 - (-2) = 6/4 = 3/2

Garis tegak lurus = m1.m2 = -1
3/2. m2 = -1
m2 = -2/3

y-y1 = m (x-x1) melalui T (-3,-4)
y - (-4) = -2/3 (x - (-3))
y+4 = -2/3 (x+3) semua sisi dikali 3
3y+12 = -2x-6
2x+3y+18 = 0