B is the midpoint of AC and D is the midpoint of CE solve for x given BD = 3x+4 and AE = 5x+19

1 answer:

5 0

It might be helpful to draw a diagram of a line in this case, but you could do this algebraically as well. The midpoint of any segment is basically the average of the two endpoints of the segment. Thus, for example, the midpoint of AC would be the value of A added to the value of C, which is then divided by 2 to get B. You just have to find all of the values for each of the letters, and then find the distance between B and D, for instance, which (the distance) may be represented as a system of equations with the statement of the distance for AE.

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Name a point that is between 50 and 60 units away from (7,-2) and state the distance between the two points.

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Let the required point be (a,b)

The distance of (a,b) from (7,-2) is

= $\sqrt{(a-7)^2+(b+2)^2}$

But this distance needs to be betweem 50 & 60

$50$

Squaring all sides

2500 < (a-7)² + (b+2)² < 3600

Let a = 7

So we have

2500 < (b+2)² <3600

b+2 < 60 or b+2 > -60 => b <58 or b > -62

Also

b+2 >50 or b + 2 < -50 => b >48 or B < -52

Let us take one value of b < 58 say b = 50

So now we have the point as (7, 50)

The other point is (7,-2)

Distance between them

= $\sqrt{(7-7)^2+(50+2)^2}= \sqrt{(52)^2}=52$

This is between 50 & 60

Hence one point which has a distance between 50 & 60 from the point (7,-2) is (7, 50)

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