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:

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

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 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

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

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