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Alexxandr [17]
3 years ago
6

Find the midpoint of the segment formed by the points D(8, 6) and E(4, 10).

Mathematics
1 answer:
bixtya [17]3 years ago
6 0
D (8, 6)
E (4, 10)

x_{midpoint} =  \cfrac{x_D+x_E}{2} = \cfrac{8+4}{2}=6 \\  \\  y_{midpoint} =  \cfrac{y_D+y_E}{2} = \cfrac{6+10}{2}=8


Answer: B. (6, 8)
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==================================================

Explanation:

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The corresponding sides pair up to form equal fractions. AB and DE form AB/DE which is equal to AC/DF, as these two sides correspond as well.

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3 years ago
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What is the equation of the line?
spin [16.1K]

Answer:

y=1/2x+2

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

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First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,2), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=2.

Also, let's call the second point you gave, (-4,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-4 and y2=0.

Now, just plug the numbers into the formula for m above, like this:

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So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

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To find b, think about what your (x,y) points mean:

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(-4,0). When x of the line is -4, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,2) and (-4,0).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

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See! In both cases we got the same value for b. And this completes our problem.

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