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Question Point Q is the centroid of AJKL. Use the given information to find the indicated measures. ​

Question Point Q is the centroid of AJKL. Use the given information to find the indicated-example-1

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Applying the centroid property to triangle AJL with Q as the centroid and AQ as the median, we find QL = (14/5) units and AL = (21/5) units.

Step 1: Recall that the centroid of a triangle divides each median into two segments, such that the ratio of the length of the shorter segment to the longer segment is 2:3.

Step 2: Apply this property to the triangle AJL, where Q is the centroid and AQ is the median. Then, we have QL:AL = 2:3, or QL = (2/3)AL.

Step 3: Substitute AQ = 21 into the equation QL + AL = AQ, and solve for AL. We get AL = (21/5) units.

Step 4: Substitute AL = (21/5) into the equation QL = (2/3)AL, and solve for QL. We get QL = (14/5) units.

Therefore, the answer is QL = (14/5) units and AL = (21/5) units.

User Nick Vanderbilt
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