Line segment ab has endpoints a(7.5, 4.2) and b(2.3, 5.4). find the coordinates of the point that divides the line segment directed from a to b in the ratio of 1: 3.

  (6.2, 4.5)

Step-by-step explanation:

That point (P) will be the weighted average of the end points, where each weight is the proportion of the segment at the end farthest from the point:

  P = (3A +1B)/(3+1)

  = (3·7.5 +2.3, 3·4.2 +5.4)/4

  = (24.8, 18)/4

  = (6.2, 4.5)

start with a line segment pq that we will copy. mark a point r that will be one endpoint of the new line segment. set the compasses' point on the point p of the line segment to be copied. adjust the compasses' width to the point q. the compasses' width is now equal to the length of the line segment pq.

step-by-step explanation: