Question

Can someone help me understand number 5 plz!!!!

Answer 1

Answer:   x = 6

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Explanation:

The picture is shown below of what's going on.

The location of point C isn't really important. What is important is the idea that if BC = 3x-8, then AB is also this length as well. The midpoint B cuts segment AC into two equal pieces AB and BC. So that's why AB = BC.

Let's find the distance from A to B

We'll use the aptly named distance formula to get this done (the pythagorean theorem is an alternative route you can take)

$A = (x_1,y_1) = (8,0)\\\\B = (x_2,y_2) = (0,6)\\\\d = \text{distance from A to B} = \text{length of segment AB}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(8-0)^2 + (0-6)^2}\\\\d = \sqrt{(8)^2 + (-6)^2}\\\\d = \sqrt{64 + 36}\\\\d = \sqrt{100}\\\\d = 10$

Therefore, segment AB is 10 units long. Segment BC is also 10 units long.

From here, we can say this:

BC = 3x-8

3x-8 = BC

3x-8 = 10

3x = 10+8

3x = 18

x = 18/3

x = 6 which is the final answer

Throughout this whole process, we never needed to know the location of point C. However, if you're curious about how to find it, then you basically would apply the midpoint formula in reverse.