Question

given: △mno
prove: the medians of △mno are concurrent
given:
steps 2, 4, & 5:

Explanation:

Step1: Recall the mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Find the mid - points of the sides of the triangle

Let's find the mid - point of side $MN$. Mid - point $P$ of $M(x_1,y_1)$ and $N(x_2,y_2)$ is $P(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Mid - point of side $NO$ and $OM$ can be found similarly.

Step3: Write the equations of the medians

The median is a line segment joining a vertex to the mid - point of the opposite side. Using the two - point form of a line $y - y_1=\frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$ for each median.

Step4: Solve the system of equations of two medians

Solve the system of equations of two of the medians to find their intersection point.

Step5: Substitute the intersection point into the third median's equation

Show that the intersection point of the first two medians lies on the third median.

Answer:

By following the above steps of finding mid - points, writing equations of medians, and solving the system of equations of medians, we can prove that the medians of $\triangle MNO$ are concurrent.