Lesson Finding a point in a segment [AB] between endpoints A and B in a coordinate plane

Finding a point in a segment [AB] between endpoints A and B in a coordinate plane

Problem 1

x-coordinate of the midpoint is the mean (half of the sum) of x-coordinates
of the points

    x-coordinate =  =  = -6.



y-coordinate of the midpoint is the mean (half of the sum) of y-coordinates
of the points

    y-coordinate =  =  = -1.



Thus the mid-point in your case is the point (-6,-1).    ANSWER

Problem 2

To move from (-5,-3) to (3,4), you should move 8 units along x-axis from -5 to 3

and (simultaneously) 7 units along y-axis from -3 to 4.



So, divide 8 units along x-axis in 5 equal parts; each part will be 8/5 = 1.6 units long.


Also, divide 7 units along y-axis in 5 equal parts; each part will be 7/5 = 1.4 units long.



Now add 1.6 to x-coordinate of the point A, and add 1.4 to y-coordinate of the point A.



Doing this way, you will obtain the coordinates of the closest to A division point 


    D = (-5+1.6,-3+1.4) = (-3.4,-1.6).     ANSWER