Questions: Use the diagram of triangle MNO where X, Y, and Z are the midpoints of the sides. If YZ = 3x + 1, and MN = 10x - 6 then YZ = ? If YX = x - 1, and MO = 3x - 7 then MO = ? #10. x = and YZ #11. x = and MO

Use the diagram of triangle MNO where X, Y, and Z are the midpoints of the sides.

If YZ = 3x + 1, and MN = 10x - 6 then YZ = ?

If YX = x - 1, and MO = 3x - 7 then MO = ?

#10. x = and YZ

#11. x = and MO

Transcript text: Use the diagram of $\triangle M N O$ where $X, Y$, and $Z$ are the midpoints the sides. If $Y Z=3 x+1$, and $M N=10 x-6$ then $Y Z=$ ? If $Y X=x-1$, and $M O=3 x-7$ then $M O=$ ? \#10. x = $\square$ and $Y Z$ \#11. x = $\square$ and MO

Solution

Solution Steps

Step 1: Setting up the equation for problem 10

The problem states that YZ = 3x + 1 and MN = 10x - 6. Since YZ connects the midpoints of two sides of triangle MNO, its length is half the length of the third side (MN). Therefore, MN = 2 * YZ. Substituting the given expressions, we get 10x - 6 = 2(3x + 1).

Step 2: Solving for x in problem 10

Simplifying the equation from Step 1, we get 10x - 6 = 6x + 2. Subtracting 6x from both sides gives 4x - 6 = 2. Adding 6 to both sides gives 4x = 8. Finally dividing both sides by 4 results in x = 2.

Step 3: Solving for YZ in problem 10

Substitute the value of x (found in Step 2) back into the expression for YZ: YZ = 3(2) + 1 = 6 + 1 = 7.