Question

Tentukan persamaan garis dan lingkaran hasil pencerminan berikut :
a. Garis: 3x-2y=12 dicerminkan terhadap garis x=5
b. Lingkaran: (x-4)²+(y-5)²=36 dicerminkan terhadap garis y=x
c. Lingkaran: x²+y²-6x+4y-36=0 dicerminkan terhadap sumbu x

Answer 1

A) (x',y') = (2(5) - x , y')
x' = 10 - x maka x = 10 - x'
y' = y
Bayangannya:
3(10 - x') - 2y' = 12
30 - 3x' - 2y' = 12
3x' + 2y' - 18 = 0
3x + 2y - 18 = 0

b) (x') = (0  1) (x)
    (y')    (1  0) (y)
x' = y
y' = x
Bayangannya:
(y' - 4)² + (x' - 5) = 36
x² + y² - 10x - 8y + 5 = 0

c) (x') = (1 0)(x)
    (y')    (0 -1)(y)
x' = x
y' = - y
Bayangannya:
x'² + (-y')² - 6x' + 4(-y') - 36 = 0
x² + y² - 6x - 4y - 36 = 0

Answer 2

A)
x' = 2(5)-x --> x' = 10-x
y' = y
3(10-x) - 2y = 12
-3x - 2y = 12 -30
-3x - 2y = - 18
3x+2y = 18
.
b)
y= x' dan x = y'
(x-4)²+(y-5)²=36 -->
(y-4)²+(x-5)²=36 atau (x-5)²+(y-4)²=36
.
c)
x --> -x
y --> -y
x²+y²-6x+4y-36=0 --> 
(-x)²+(-y)²-6(-x) +4(-y) -36=0
x²+y²+6x - 4y-36=0