Part (a)
Initialize
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Tools≻Load Package: Student Precalculus
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Loading Student:-Precalculus
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Obtain the area of
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Context Panel: Assign to a Name≻
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Obtain
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Apply the Line command from the Student Precalculus package.
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Write
Context Panel: Assign Function
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Obtain
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Apply the Line command from the Student Precalculus package.
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Write
Context Panel: Assign Function
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Calculate
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Expression palette: Definite-integral template
Press the Enter key.
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Context Panel: Simplify≻Simplify
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Calculate
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Expression palette: Definite-integral template
Press the Enter key.
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Context Panel: Simplify≻Simplify
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Thus, the centroid is the point .
Next, obtain the midpoints of the three sides of and the three medians of , then intersect the medians.
Part (b)
Midpoints
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Apply the Midpoint command from the Student Precalculus package.
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Medians
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Apply the Line command from the Student Precalculus package.
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Intersect medians and
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Apply the solve command.
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Evaluate median at
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Write and press the Enter key.
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Context Panel: Evaluate at a Point≻
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Medians and intersect at the centroid, and median also passes through the centroid.