Chapter 14.5, Problem 24WE

a.

To determine

To complete the statement.

Answer to Problem 24WE

The complete statement is $\frac{XG}{XM}=\frac{2}{3}$ .

Explanation of Solution

Given information:

G is the intersection of the medians of triangle XYZ.

  

The statement is: $\frac{XG}{XM}=?$

The medians of a triangle intersect in a point that is two-thirds of the distance from each vertex to the mid-point of the opposite side.

Hence, the complete statement is $\frac{XG}{XM}=\frac{2}{3}$ .

b.

To determine

To complete the statement.

Answer to Problem 24WE

The complete statement is $\frac{GM}{GX}=\frac{1}{2}$ .

Explanation of Solution

Given information:

G is the intersection of the medians of triangle XYZ.

  

The statement is: $\frac{GM}{GX}=?$

The medians of a triangle intersect in a point that is two-thirds of the distance from each vertex to the mid-point of the opposite side.

Hence, the complete statement is $\frac{GM}{GX}=\frac{1}{2}$ .

c.

To determine

To state what dilation maps X to M.

Answer to Problem 24WE

The dilation $D_{G,\frac{1}{2}}$ maps X to M.

Explanation of Solution

Given information:

G is the intersection of the medians of triangle XYZ.

  

The dilation $D_{G,\frac{1}{2}}$ maps X to M.

d.

To determine

To state what is the image of Y and Z under this dilation.

Answer to Problem 24WE

The image of Y and Z under the dilation $D_{G,\frac{1}{2}}$ is $\frac{1}{3}$ .

Explanation of Solution

Given information:

G is the intersection of the medians of triangle XYZ.

  

The image of Y under the dilation $D_{G,\frac{1}{2}}$ is $\frac{1}{3}$ .

The image of Z under the dilation $D_{G,\frac{1}{2}}$ is $\frac{1}{3}$ .