## j814wong 3 years ago Let A,B, and C be three points in a plane such that AB:BC = 3:5. Which of the following can be the ratio of AB:AC? I. 1:2 II. 1:3 III. 3:8 A. I only B. II only C. III only D. I and III only E. I, II, and III

1. amistre64

might help to draw it out

2. amistre64

|dw:1343938402235:dw|

3. amistre64

write the ratios as fractions so see if any of them are equal to each other as well

4. j814wong

Oh I see. So 3:8 works. And 1:2 also works if I draw it this way.|dw:1343939315480:dw| Thanks. I guess where I was thrown off was that the question said three points on a plane instead of line.

5. amistre64

ab:ac 3 : 2 3/2 not equal to 1/2 tho

6. amistre64

but, what if they form a triangle instead of a line?

7. amistre64

|dw:1343939637228:dw|

8. j814wong

If that happens, how should I go about it?

9. amistre64

a triangle has the property that the sum of 2 sides is greater than the remaining side

10. amistre64

|dw:1344178277031:dw| AC would be bounded between 2 and 8

11. amistre64

therefore our ratio is bounded between: 3/2 and 3/8 3/2, 1 : .666 3/3, 1 : 1 3/4, 1 : 1.333 3/5, 1 : 1.666 3/6, 1 : 2 3/7, 1 : 2.333 3/8, 1 : 2. 666

12. amistre64

or we could just take the 3 options and get them to the 3 : n ratio .... 3:6 3:9 3:8 since 3:9 is out of bounds, and the other 2 are in bounds, it would appear to me to be I and III