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
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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) (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) (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)
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