Question

Need answer fast please

Answer 1

The correct equation that relates DM to MK is:

C.
`\[ MK = (1)/(2) DM \]`

To find the relationship between DM and MK in terms of x and y, we can use the properties of a centroid. The centroid of a triangle divides each median into two segments, with the segment toward the vertex being twice as long as the segment toward the opposite side.

Given that DM = 8, MJ = 2y, and EM = 6, we can express MJ in terms of DM and EM:

`\[ MJ = DM - DJ \]`

`\[ 2y = 8 - DJ \]`

Solving for DJ, we get:

`\[ DJ = 8 - 2y \]`

Now, considering the centroid property, we know that \( MJ = 2 \times MK \). Therefore:

`\[ 2y = 2 * MK \]`

Solving for MK:

`\[ MK = y \]`

Now, looking at the other side of the centroid, we can express FM in terms of DM and EM:

`\[ FM = EM - EF \]`

`\[ 2x = 6 - EF \]`

Solving for EF:

`\[ EF = 6 - 2x \]`

Again, using the centroid property, we know that \( FM = 2 \times MK \). Therefore:

`\[ 2x = 2 * MK \]`

Solving for MK:

`\[ MK = x \]`

Now, we need to find the relationship between DM and MK. From the above, we have:

`\[ MK = x \]`

So, the correct option is:

`\[ \mathbf{C.} \ MK = (1)/(2) DM \]`