## anonymous 4 years ago find b given that: A(4,10) and B(b,7) are 5 units apart. How can i solve it ?

1. anonymous

distance formula$5=\sqrt(4-b)^2+(10-7)^2$ that sqrt should be over the whole right side

2. anonymous

then solve for b

3. anonymous

b=8 or b=0 there are 2 possibilities.

4. anonymous

So it would be 5 = 4-b + 9?

5. anonymous

could you show how you got your results?

6. anonymous

please cause i have 4 problems like this

7. anonymous

the (4-b) is still square and the right side should still be under the sqrt

8. anonymous

yeah

9. anonymous

$5=\sqrt((4-b)^2+(10-7)^2)$ $25=(4-b)^2+9$ subtract 9$16=(4-b)^2$ take the squareroot, and remember that when taking the squareroot you have to use the negative and positive$\pm4=4-b$

10. anonymous

can you complete from there? or want me to finish?

11. anonymous

12. anonymous

sorry! im just a better learning seeing it out solved

13. anonymous

so you have$4=4-b$ subtract 4 and multiply by -1 to get rid of the negative $0=b$ and you also have$-4=4-b$ subtract 4$-8=-b$ and multiply by -1 to get rid of the negative $8=b$

14. anonymous

I don't mind. Everyone learns differently and I'm happy to help.

15. anonymous

thank you but i have one more

16. anonymous

the question is

17. anonymous

A(b,b) is sqrt(18) units from its origin.

18. anonymous

find b

19. anonymous

the origin is at (0,0) so assuming the b is the same you have$\sqrt18=\sqrt{(b-0)^2+(b-0)^2}$

20. anonymous

so$\sqrt{18}=\sqrt{b^2+b^2}$ $\sqrt{18}=\sqrt{2b^2}$square both sides $18=2b^2$divide by 2 $9=b^2$take the square $\pm3=b$root

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