Hey there! I'm happy to help!
First of all, don't worry so much about struggling with something difficult! It's part of the human experience. Our minds are wired to be challenged but then when we push through and have faith in ourselves that's how we grow and improve!
What we are dealing with here are lines. We are being given the coordinates for one endpoint of a line and a midpoint and we want to find the other endpoint.
Let's just go one-dimensional first to make this easier to understand. Imagine that you have a number line. You draw a line going from 1 to 7. So, 1 and 7 are the two endpoints. Your midpoint is going to be halfway between those two. To find the middle of anything, you just add the two numbers and divide them by two.
1+7=8
8/2=4
So, 4 is our midpoint in this situation.
So, what if we just had our endpoint 1 and our midpoint 4? Well, we see that we go forward three spaces to get to 4. Now we are halfway! Then, we just do another three to make it to our finish line, which is 7. Or, we just take that distance and multiply it by two! This is related to our divide by two rule but just backward!
So, let's look at these problems.
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A.
We have the coordinates of our line here. Our endpoint is (1,-9) and our midpoint is (4,-1). Remember what we did with our number line? We are basically going to do it with our x and y values.
So, to go from our endpoint 1 to 4 we go three spaces. If we go another 3 spaces, it will be 7. So, our x-value is 7.
With our y-values, we go from -9 to -1, so we climb 8 spaces. If we add another 8 spaces we will end up at 7, so our y-value is 7 again!
So, our other endpoint is (7,7)!
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B.
To go from -2 to 9 is adding 11, so we add another 11 to 9 to give us an x-value of 20.
Going from 19 to 2 is subtracting 17, so we need to subtract another 17, which gives us a y-value of -15.
So, our endpoint is going to be (20, -15).
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Have a wonderful day and keep on learning! :D
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