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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 16 Page 464

Look for the centroid of the triangle.

(3,4)

Practice makes perfect

To balance the triangles, Georgia needs to hang the them by their centroids. The centroid is the intersection point of the medians. Let's find two medians and find their intersection.

Median Through Vertex A

The median through vertex A goes through the midpoint of BC.

We can find the midpoint using the Midpoint Formula.

M=(x_1+x_2/2,y_1+y_2/2)

SubstitutePoints

Substitute ( 3,8) & ( 6,0)

M=(3+ 6/2,8+ 0/2)

Add terms

M=(9/2,8/2)

Calculate quotient

M=(4.5,4)

Putting this point on the coordinate plane, we can see that the median connecting point A and this midpoint is horizontal.

Median Through Vertex B

Let's repeat this process to find the median through vertex B, which also goes through the midpoint of AC.

We can find the midpoint using the Midpoint Formula.

M=(x_1+x_2/2,y_1+y_2/2)

SubstitutePoints

Substitute ( 0,4) & ( 6,0)

M=(0+ 6/2,4+ 0/2)

Add terms

M=(6/2,4/2)

Calculate quotient

M=(3,2)

Putting this point on the coordinate plane, the median connecting point B and this midpoint is vertical.

Finding the Centroid

From the graph with both medians we see that the intersection point is (3,4).

To keep the triangles horizontally in balance, Georgia should hang them at their centroid, at the point (3,4).

Subchapter links

1 Bisectors of Triangles p.464

2 Medians and Altitudes of Triangles p.464

3 Inequalities in One Triangle p.465

4 Indirect Proof p.465

5 The Triangle Inequality p.466

6 Inequalities in Two Triangles p.466