Question

in triangle dfe, kj = 50 units. what is the length of segment ek? 25 units 50 units 100 units 150 units figure may not be drawn to scale

Explanation:

Step1: Recall centroid property

The centroid of a triangle divides each median in a 2:1 ratio. Point K is the centroid of triangle DFE and DJ is a median. The centroid K divides the median DJ such that DK = 2KJ and KJ is the shorter segment from the centroid to the side - mid - point.

Step2: Identify given length

Given that KJ = 50 units.

Step3: Find DK

Since DK = 2KJ, then DK=2×50 = 100 units.

Step4: Recall median property

The median DJ divides the side FE into two equal parts at J. Also, the centroid K lies on the median DJ. We know that the distance from the vertex E to the centroid K (EK) is equal to the distance from the vertex D to the centroid K (DK).

Answer:

100 units