Section and Mid-Point Formulae — Part 2: Mid-points and the centroid: visual lesson, ICSE Class 10 Mathematics

Lesson

Section and mid-point formulae, Part 2

The mid-point is the $1 : 1$ section point. Join each vertex of a triangle to the mid-point of the opposite side and the three medians meet at the centroid.

In this lesson you will

Find the mid-point of a segment
Find an end point when the other end and the mid-point are given
Use mid-points to find the fourth vertex of a parallelogram
Find the centroid of a triangle, a missing vertex from the centroid, and the vertices from the mid-points of the sides

triangle KLM
median from K
median from L
median from M

The three medians meet at one point, the centroid $G(1, 1)$.

Concept

What you will be able to do

Find the mid-point of a segment
Find an end point from the other end and the mid-point
Find the fourth vertex of a parallelogram
Find the centroid, a missing vertex, and vertices from mid-points of sides

Concept

The mid-point formula

Put $m_1 = m_2$ in the section formula: the mid-point of $A(x_1, y_1)$ and $B(x_2, y_2)$ is the average of the ends.

M\left(\dfrac{x_1 + x_2}{2}, \ \dfrac{y_1 + y_2}{2}\right)

segment AB

$M$ is the average of the ends: $\left(\dfrac{-4 + 6}{2}, \dfrac{-1 + 5}{2}\right) = (1, 2)$.

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