Point a is located at (2, 8) and point b is located at (8, 5). what point partitions the directed line segment ab¯¯¯¯¯ into a 1: 3 ratio? (2 1/2, 3 1/4) (3 1/3, 4 1/3) (3 1/2, 7 1/4) (6 1/2, 5 1/4)

(3 1/2, 7 1/4)

Step-by-step explanation:

A 1:3 ratio means we want 4 equal parts  (1+3 = 4)

Find the distance of the segment and divide by 4

(x2+x1)/4,  (y2+y1)/4

(8-2)/4 , (5-8)/4

6/4, -3/4

Since the first part is of ratio 1, we multiply by 1

Now add this to the starting point

(2 + 6/4, 8+ -3/4)

Getting a common denominator of 4

2*4/4 = 8/4

8 *4/4 = -3/4

(8/4 + 6/4, 32/4 -3/4)

(14/4, 29/4)

Now change back to a mixed number

(3 2/4 , 7 1/4)

(3 1/2, 7 1/4)