Find the coordinates of point B that lies along the directed line segment from A(-5, 2) to C(11, 0) and partitions the segment in the ratio of 5:3.

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

  x, y  =  5, 3/4

Step-by-step explanation:

4038

step-by-step explanation:

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solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b