The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

Asked by Pragya Singh | 11 months ago |  86

##### Solution :-

Vertices of ΔPQR i.e. P (2, 1), Q (-2, 3) and R (4, 5)

Let RL be the median of vertex R.

So, L is a midpoint of PQ.

We know that the midpoint formula is given by

$$(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})$$

$$(\dfrac{2-2}{2}, \dfrac{1+3}{2})$$  = (0, 2)

We know that the equation of the line passing through the points (x1, y1) and (x2, y2) is given by
$$y-5= \dfrac{2-5}{0-4}(x-4)$$

$$y-5= \dfrac{-3}{-4}(x-4)$$

(-4) (y – 5) = (-3) (x – 4)

-4y + 20 = -3x + 12

-4y + 20 + 3x – 12 = 0

3x – 4y + 8 = 0

The equation of median through the vertex R is 3x – 4y + 8 = 0.

Answered by Abhisek | 11 months ago

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