Answer:
B ( 5 , 3/4 )
Step-by-step explanation:
Solution:-
We are given two points in the cartesian coordinate system as:
A ( -5 , 2 ) C ( 11, 0 )
The point B lies on the line segment from A to C. The ratio of segment given is:
AB / BC = 5 / 3
To solve such type of problems. We will use vector equation of line AC.
To form a vector equation of line representing AC. We will first determine the direction vector ( d ) that is parallel to the line AC as follows:
d = OC - OA
d = < 11, 0 > - < -5,2 >
d = < 16 , -2 >
The fixed point on the line is taken. We will take point A. The vector equation of line from point A to point C is expressed as:
< x , y > = OA + t*d
< x , y > = < -5, 2 > + t* < 16 , - 2 >
The above equation satisfies all the points that lies on the line AC. To determine the coordinates of ( B ). We will plug in the appropriate value of parameter ( t ) and evaluate. We are given the ratio 5:3.
So point B is 5/8 th the magnitude of the distance AC from A. Hence, t = 5/8 as follows:
< x , y > = < -5 , 2 > + ( 5/8 ) * < 16 , -2 >
< x , y > = < -5 , 2 > + < 10 , -5/4 >
< x , y > = < 5 , 3/4 > ... Answer
