## LilVeroDez13 3 years ago Suppose B is the midpoint of AC. AB = 5x and BC = 3x + 4. Find AB. (Hint: Make a sketch and write an equation to solve.)

1. jim_thompson5910

B is the midpoint, so AB and BC are equal pieces that make up AC

2. jim_thompson5910

this means AB = BC 5x = 3x+4

3. LilVeroDez13

So then i would solve for x?

4. jim_thompson5910

yes you would

5. jim_thompson5910

tell me what you get

6. LilVeroDez13

I get .5.. but i know thats wrong.. so, 5x = 3x + 4.. u combine like terms.. right?

7. jim_thompson5910

subtract 3x from both sides

8. jim_thompson5910

5x = 3x + 4 5x-3x = 3x + 4-3x 2x = 4

9. jim_thompson5910

whats next?

10. LilVeroDez13

divide 2 do both sides.. x = 2

11. jim_thompson5910

exactly, now use this to find AB

12. LilVeroDez13

5(2) = 10 :)

13. jim_thompson5910

you nailed it

14. LilVeroDez13

Thanks!! :) Can u help me with another question

15. jim_thompson5910

sure

16. LilVeroDez13

Thanks!! :)) Four points A, B, C, and D are coplanar, but only two at a time are collinear. Suppose a line is drawn through each pair of points. How many lines can you draw?

17. jim_thompson5910

Four points A, B, C, and D are coplanar means that all four points lie in the same plane

18. jim_thompson5910

but only two at a time are collinear means that all 4 points do NOT form a straight line also, it means that there are no 3 points that form a straight line

19. jim_thompson5910

so we might have something like this |dw:1348964739339:dw|

20. jim_thompson5910

Here are two pairs of lines |dw:1348964798916:dw|

21. jim_thompson5910

oops just meant to say "here are a pair of lines"

22. jim_thompson5910

Here's another pair |dw:1348964855161:dw|

23. jim_thompson5910

and another pair |dw:1348964897439:dw|

24. jim_thompson5910

and that's all we can draw because there are no other possible pairs of lines to draw

25. LilVeroDez13

:) So, there are 4 possible ways?

26. jim_thompson5910

double that to get 8

27. jim_thompson5910

4 pairs of lines = 8 lines

28. LilVeroDez13

Ahh.. i see now. Thanks so much!! ur really smart :) geometry kicks my butt. You make it easy to understand :)

29. jim_thompson5910

oh wait, i'm counting 3 pairs (not sure where I got 4 pairs) so 3 pairs = 6 lines

30. jim_thompson5910