Someone please help me

Question

Line segment AB has endpoints (7, 2) and (4, 6). What are the coordinates of the point that divides AB in the ratio of 2:3?

1. 1Choice 1
2. (5.8, 3.6)
3. 2Choice 2
4. (2.2, 1.6)
5. 3Choice 3
6. (5, 4.8)
7. 4Choice 4
8. (2.6, 1.2)

Answer 1

choices 2 and 4 can be eliminated,

as they both have a coordinate that isn't even inside the endpoints

1.6 and 1.2 are outside the endpoint limits

that leaves choice 1 or 3 as the only possible correct answers

7-4 = 3

2/5 x 3 = 6/5 = 1.2, 7-1.2 = 5.8

6-2 = 4

2/5 x 4 = 8/5 = 1.6, 2+1.6 = 3.6

choice 1 looks correct, and the only

correct choice among the four (5.8, 3.6)

(4,6) and (7,2) are two points on the line 4x+3y =34

plug in (5.8, 3.6)

it works

choice 1 is correct

but so is choice 5 (which isn't there but could have been)

choice 5 is correct

had its point been (5.2, 4.4)

4(5.2) + 3(4.4) = 20.8 + 13.2 = 34

it works too.

when you divide the line segment into 2 parts in a 2:3 ratio, it doesn't specify

which part is 2/5 of the segment and which is 3/5 of it, so you have 2 possible

correct points, either (5.8,3.6) or (5.2,4.4)

midpoint of the line segment is (5.5, 4) 5.5 is half way between 5.8 and 5.2

4 is halfway between 4.4 and 3.6

Answer 2

Since ratio 2:3, need to determine point 2/5 of the way between A(7,2) and B(4,6).

Determine x coordinate 2/5 of way between 7 and 4:

(4-7)*2/5 + 7 = 5.8

Determine y coordinate 2/5 of way between 2 and 6:

(6-2)*2/5 + 2 = 3.6

coordinates are (5.8,3.6) choice 1