Q) A(3, 0), B(6, 4) and C(-1, 3) are vertices of a triangle ABC. Find length of its median BE.

Ans: Let’s plot the points on the graph:

Step 1:  To draw median BE, point E lies on AC

Let’s consider the coordinates of E are (x, y)

Since E is the midpoint of A C, we will find out the coordinates of E.

We know that the coordinates of mid point of 2 coordinates (X₁, Y₁) and (X₂, Y₂) given by:

(X, Y) =

∴ value of coordinates of midpoint E of A (3, 0) and C(- 1, 3) are:

(X, Y) =

=

Step 2: Next, we find out the length of line BE, where B is (6, 4) and E is (1, )

We know that the distance between two points (X₁, Y₁) and (X₂, Y₂) is given by:

S = √ [(X₂ – X₁)² + (Y₂ – Y₁)^{2 ]}

∴  BE =

=

= units

Therefore, the length of the median BE is units.

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