## anonymous 4 years ago One of the endpoints of the base of a triangle is at P(4, 5). The midpoint of the base is at (1, 1). Erik performed the steps shown to find the coordinates of the other endpoint of the base. Step 1. x1 = 4, y1 = 5, x = 1, y = 1 Step 2. Step 3. Step 4. 2 = 4 + x2, 2 = 5 + y2 Step 5. 0 = 4 + x2 , 0 = 5 + y2 Step 6. x2 = -4, y2 = -5 In which step did Erik first make an error? Answer Step 2, because he used the formula to find the length of a line segment. Step 3, because he substituted the values incorrectly in the formula Step 4, because he multiplied both the equat

1. anonymous

does step 4 pr 5 look wronf i cant figure out how t owrite out step 2 and 3

2. amistre64

how would you determine the midpoint? match that to the ficticious persons method and see what fits

3. amistre64

or end points or whatever the questions asking ....

4. anonymous

step two is the midpoint between two point formula and step three is the same but puting in the numbers

5. amistre64

Midpoint - endpoint given is the distance and direction to the end point: (M-P) add that result to the midpoint to go the same distance and direction further: M+(M-P) = 2M-P for the other end point

6. anonymous

so step 4 would be wrong?

7. amistre64

2M = (2 , 2) - P = (-4,-5) ------------- (-2,-3) is what I get

8. anonymous

okay but i have to find out what step is wrong thats what i dont get

9. amistre64

i dont do the ficticious persons steps, so I really cant say wear they messed up at .... and it would help to know what step 2 and 3 actually were

10. amistre64

maybe a formula?

11. amistre64

$\left(\frac{Mx-Px}{2}, \frac{My-Py}{2}\right)$

12. amistre64

that doesnt quite jive ....

13. amistre64

$(Mx,My)=\left(\frac{Px+Ex}{2}, \frac{Py+Ey}{2}\right)$ that might seem better

14. amistre64

M for midpt, P for given Point, and E for other endpt

15. anonymous

|dw:1328202827251:dw|

16. anonymous

i hope u understand that lol i tried

17. amistre64

is step 2: x1-x2 ? if so then its not the midpt formula

18. anonymous

no it x1 plus x2

19. amistre64

the midpt is an average of 2 points; an average is sum up the points and divide by ...well 2 since htere are only 2 points :)

20. amistre64

then step 2 looks fine if its addition

21. anonymous

okay so its 3 4 or 5 lol i hate this thank u for workn with me ot figure it out

22. amistre64

step 3 is plugging in values and with addition it doesnt matter what goes where since 4+5 = 5+4

23. anonymous

okay sooo three is wrong im confused

24. amistre64

3 is fine

25. amistre64

4 is fine, sicne 2*1 = 2 in both accounts

26. amistre64

there is no reason for making step 5 zero out

27. anonymous

okay :) lol thank u wait so if we are doing addition we shouldnt do subtraction right

28. amistre64

well, if we add, then subtracting is really not a good idea unless you subtract the right value :) 4+5 = 4--5

29. amistre64

rides here, good luck :)

30. amistre64

my bet is step 5 tho

31. anonymous

thank u soo much