Which equation has intercepts x(1, 0, 0), y(0, -1, 0), and z(0, 0, 2)?
3x-2y+6z=12
2x-2y+z=2
4x-4y+z=4
x-y+2z=4
My answer- 2x-2y+2=2
That does not work: 2(1)-2(-1)+2 = 6
Better try again.
4x-4y+z+4?
I don't see any choices which work. I suspect a typo.
There was no typo, I had just submitted my quiz and the choice I originally picked was correct.
4(1)-4(-1)+2 = 4+4+2 = 10
??
To determine which equation has intercepts x(1, 0, 0), y(0, -1, 0), and z(0, 0, 2), we can substitute the coordinates of each intercept into the given equations to check if they satisfy the equation.
Let's substitute the coordinates of intercept x(1, 0, 0) into each equation:
Equation 1: 3(1) - 2(0) + 6(0) = 3, which is not equal to 0.
Equation 2: 2(1) - 2(0) + 1(0) = 2, which is not equal to 0.
Equation 3: 4(1) - 4(0) + 1(0) = 4, which is not equal to 0.
Equation 4: 1 - 0 + 2(0) = 1, which is not equal to 0.
Now let's substitute the coordinates of intercept y(0, -1, 0) into each equation:
Equation 1: 3(0) - 2(-1) + 6(0) = 2, which is not equal to 0.
Equation 2: 2(0) - 2(-1) + 1(0) = 0, which is equal to 0.
Equation 3: 4(0) - 4(-1) + 1(0) = 0, which is equal to 0.
Equation 4: 0 - (-1) + 2(0) = -1, which is not equal to 0.
Finally, let's substitute the coordinates of intercept z(0, 0, 2) into each equation:
Equation 1: 3(0) - 2(0) + 6(2) = 12, which is not equal to 0.
Equation 2: 2(0) - 2(0) + 1(2) = 2, which is equal to 0.
Equation 3: 4(0) - 4(0) + 1(2) = 2, which is not equal to 0.
Equation 4: 0 - 0 + 2(2) = 4, which is not equal to 0.
From the above calculations, we see that only equation 2: 2x - 2y + z = 2 satisfies all three intercepts. Therefore, equation 2 is the correct answer.
Your answer, 2x - 2y + 2 = 2, is incorrect, as it does not satisfy the given intercepts.