Answer:
The distance of the midpoints of AB and CD is 24 cm
Explanation:
The given information are;
The length of AD = 36 cm.
C and B are points on AD
The ratio of AB:BC:CD 2:3:4
The distance of the midpoints of segments AB and CD required
Therefore, we have the following proportion of the total length, 36
Segment AB = 2/(2 + 3 + 4) = 2/9×36 = 8 cm
Segment BC = 3/(2 + 3 + 4) = 3/9×36 = 12 cm
Segment CD = 4/(2 + 3 + 4) = 4/9×36 = 16 cm
The x-coordinate of the midpoint of segment AB = 4 cm
The x-coordinate of the midpoint of segment CD = 8 + 12 + 16/2 = 28 cm
Which gives;
The distance of midpoint of segment AB from A = 4 cm
The distance of midpoint of segment CD from A = 28 cm
And the distance of the midpoints of AB and CD = 24 - 4 = 24 cm.