Question

A segment with endpoints A (2, 1) and C (4, 7) is partitioned by a point B such that AB and BC form a 3:2 ratio. Find B.

Answer 1

please explain so i know how to do it?

Answer 2

@SolomonZelman can you help?

Answer 3

so i need to find the length between the points first?

Answer 4

yep, and this is one way to solve

Answer 5

okay give me a second to figure it out lol

Answer 6

so the length is 6.32?

Answer 7

perfect

Answer 8

but how did you find where b is suppose to be?

Answer 9

the ratio of AB to BC
the sum of the 2 segments = the total length
and the ratio of size to one another is 3:2

so 3 segments of AB = 2 segments of BC

now solve using simultaneous equations

AB = z
BC = w

z + w = 6.32 EQN 1
and
3z = 2w EQN 2

this will let you solve the length of AB and BC

do this, then we'll solve for B's coordinates (x,y)

Answer 10

b is 3/5 the distance from a

Answer 11

yep, so length A to B = ?

Answer 12

6.32, right?

Answer 13

that's total length
we're lookin for A to B length

Answer 14

3.792?

Answer 15

these really confuse me lol

Answer 16

all good
so A to B is 2 fifths of 6.32
A to B = 2.53

therefore B to C is 3 fifths of 6.32
B to C = 3.79