Q:

The endpoints of line MP are M(1,4) and P(16,14). If A partitions line MP in a ratio of MA: AP=2: 1, which of the following represents the coordinates of point A?A(6,9)B(7,8)C(11,32/3)D(9,6)

Accepted Solution

A:
we have that
point M(1,4)
and
point P(16,14)

the distance MP 
in the x coordinate is
d MPx=(16-1)-----> 15 units

the distance MP 
in the y coordinate is
d MPy=(14-4)-----> 10 units

the coordinate of point A
in the x coordinate
Mx=1----------> the x coordinate of the point M
Ax=Mx+(2/3)*d MPx-------> 1+(2/3)*15------> Ax=11

the coordinate of point A
in the y coordinate
My=4----------> the y coordinate of the point M
Ay=My+(2/3)*d MPy-------> 4+(2/3)*10------> (12+20)/3------> Ay=32/3

the coordinates of point A is (11,32/3)

the answer is the option
C(11,32/3)