SOLUTION: a directed line segment AB with A(1,3) and B(8,4) is partitioned by point C such that AC and CB form a 1:4 ratio. find C. write answer as a coordinate point round to nearest ten

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: a directed line segment AB with A(1,3) and B(8,4) is partitioned by point C such that AC and CB form a 1:4 ratio. find C. write answer as a coordinate point round to nearest ten      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1131197: a directed line segment AB with A(1,3) and B(8,4) is partitioned by point C such that AC and CB form a 1:4 ratio. find C.
write answer as a coordinate point
round to nearest tenth if needed
Found 2 solutions by solver91311, greenestamps:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let C be represented by the ordered pair , then the horizontal distance from A to C, namely , because of the proportionality of the sides of similar triangles must be in a 1:4 ratio with the horizontal distance from C to B, namely . Hence, we can write:



Solve for to obtain the abscissa of point C. The other coordinate is found in a similar fashion.


John

My calculator said it, I believe it, that settles it

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


With the ratio AC:CB = 1/4, point C is 1/5 of the way from A to B.

The x and y coordinates of point C are each 1/5 of the way from the x and y coordinates of A to the x and y coordinates of B.

Difference in x coordinates from A to B = 7; 1/5 of 7 = 7/5 = 1.4; x coordinate of C = 1+1.4 = 2.4

Difference in y coordinates from A to B is 1; 1.5 of 1 is 1/5 = 0.2; y coordinate of C = 3+0.2 = 3.2.

ANSWER: C = (2.4,3.2)