Question

If Q is the centroid of AJKL, LN = 72. JP = 93.

and MK = 78, find each measure.
30 798
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M
L
N
2
P
K
a) LQ =
b) QN =
c) QP =
d) JQ =
e) QK =

Answer 1

The lengths of the segments connecting to the centroid Q of triangle AJKL are determined using the property that a centroid divides the medians in a 2:1 ratio. The calculations give the lengths of LQ, QN, QP, JQ, and QK as 48, 24, 62, 31, and 52 units, respectively.

Step-by-step explanation:

To solve for the various lengths in the question involving centroid Q of triangle AJKL, we will apply the concept that the centroid of a triangle divides the medians in a 2:1 ratio, with the centroid being twice as far from the vertex as it is from the midpoint of the opposite side.

1. LQ = 2/3(LN) = 2/3(72) = 48 units
2. QN = 1/3(LN) = 1/3(72) = 24 units
3. QP = 2/3(JP) = 2/3(93) = 62 units
4. JQ = 1/3(JP) = 1/3(93) = 31 units
5. QK = 2/3(MK) = 2/3(78) = 52 units