3,1
Mark my answer a brainliest answer question
In order to find the second endpoint or a line segment given the first and the midpoint, you need to realize that the midpoint is an average of the two endpoints. Given that fact, we can derive this formula looking at x values of points A and B with midpoint M. Remember this is only looking at the x values.
(A + B)/2 = M
So if we are looking for A, we can solve for A and use this modified formula.
(A + B)/2 = M
A + B = 2M
A = 2M - B
Now we can do this with the y values of these points as well. We then have the coordinates of both parts of A.
Original height = original width = x mm
1. She made an enlarged copy...
height = 2x
width = 2x
2. She cut off a rectangle...
height = 2x
width =
3.She doubled the width...
height = 2x
width =
height * width = area
Original height was
162 mm
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.
