A(3, 0), B(6, 4) and C(-1, 3) are vertices of a triangle ABC.

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) = $(\frac{(X_1 + X_2)}{2}, \frac{(Y_1 + Y_2)}{2})$

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

(X, Y) = $(\frac{(3 - 1)}{2}, \frac{(0 + 3)}{2})$

= $(1, \frac{3}{2})$

Step 2: Next, we find out the length of line BE, where B is (6, 4) and E is (1, $\frac{3}{2}$ )

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

S = √ [(X₂ – X₁)² + (Y₂ – Y₁)^{2 ]}

∴ BE = $\sqrt{(6 - 1)^2 + (4 - \frac{3}{2})^2}$

= $\sqrt{(25 + \frac{25}{4})}$

= $\frac{5}{2} \sqrt 5$ units

Therefore, the length of the median BE is $\frac{5}{2} \sqrt 5$ units.

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