B.) (1,1) (2,5) should be your answer.
J, K, and L are collinear
J is between K and L
LK = KJ + LJ
LK = 9x + 7
KJ = 2x - 3
LJ = 4x - 8
9x + 7 = (2x - 3) + (4x - 8)
9x + 7 = (2x + 4x) + (-3 - 8)
9x + 7 = 6x + -11
9x + 7 = 6x - 11
9x + 7 - 7 = 6x - 11 - 7
9x = 6x - 18
9x - 6x = 6x - 6x - 18
3x = -18
x = -6
∴ The value of x is -6
Answer:
Step-by-step explanation:
Firstly, note that -2i really is just z = 0 + (-2)i, so we see that Re(z) = 0 and Im(z) = -2.
When we're going from Cartesian to polar coordinates, we need to be aware of a few things! With Cartesian coordinates, we are dealing explicitly with x = blah and y = blah. With polar coordinates, we are looking at the same plane but with angle and magnitude in consideration.
Graphing z = -2i on the Argand diagram will look like a segment of the y axis. So we ask ourselves "What angle does this make with the positive x axis? One answer you could ask yourself is -90°! But at the same time, it's 270°! Why do you think this is the case?
What about the magnitude? How far is "-2i" stretched from the typical "i". And the answer is -2! Well... really it gets stretched by a factor of 2 but in the negative direction!
Putting all of this together gives us:
z = |mag|*(cos(angle) + isin(angle))
= 2*cos(270°) + isin(270°)).
To verify, let's consider what cos(270°) and sin(270°) are.
If you graph cos(x) and look at 270°, you get 0.
If you graph sin(x) and look at 270°, you get -1.
So 2*(cos(270°) + isin(270°)) = 2(0 + -1*i) = -2i as expected.
R=7 because you would do -49 divided by -7
