Answer:
C ( 11 , -11 )
Step-by-step explanation:
Solution:-
We are given two points in the cartesian coordinate system as:
A ( 3 , -5 ) B ( 13 , -15 )
The point C lies on the line segment from A to B. The ratio of segment given is:
AC / AB = 4 / 5
To solve such type of problems. We will use vector equation of line AC.
To form a vector equation of line representing AB. We will first determine the direction vector ( d ) that is parallel to the line AB as follows:
d = OB - OA
d = < 13 , -15 > - < 3 , -5 >
d = < 10 , -10 >
The fixed point on the line is taken. We will take point A. The vector equation of line from point A to point B is expressed as:
< x , y > = OA + s*d
< x , y > = < 3, -5 > + s* < 10 , -10 >
The above equation satisfies all the points that lies on the line AB. To determine the coordinates of ( C ). We will plug in the appropriate value of parameter ( s ) and evaluate.
So point C is 4/5 th the magnitude of the distance AB from A. Hence, s = 4/5 as follows:
< x , y > = < 3 , -5 > + ( 4/5 ) * < 10 , -10 >
< x , y > = < 3 , -5 > + < 8 , -8 >
< x , y > = < 11 , -11 > ... Answer
