Grace has a segment with endpoints a(3, 2) and b(6, 11) that is partitioned by a point c such that ac and bc form a 2: 3 ratio. she knows that the distance between the x-coordinates is 3 units. which of the following fractions will let her find the x-coordinate for point c? (6 points) 3 over 5 3 over 2 2 over 3 2 over 5 i just want to confirm my answer

answer:

option d -2 over 5

step-by-step explanation:

given: let point divides the join of point and point

the ratio of 2: 3 is for the length of segment ac to the length of segment cb.

⇒ the ratio of the length of segment ac to the length of segment ab is 2: 5.

therefore,point c is 2/5 of the way from a to b

so the fraction is 2/5.

then, using section formula

similarly,  

therefore,        

and option d is correct 2 over 5.

.5 lb

step-by-step explanation:

12 in / 6 in =2 in

.25 x 2 = .5 lb