Question

18th question...answer plz

Answer 1

We know that : Median of a Triangle is the Line joining the Vertex of a Triangle to the Mid point of the Opposite Side.

The Given Question asks about the Length of the Median Joining Vertex (A) to the Opposite Side (BC)

From the Definition of Median, We can Realize that, The Median from Vertex (A) must join the Mid point of Side (BC)

Given : The Vertices of Side (BC) are B(1 , 5) and C(-3 , -1)

We know that, Mid point of a Line joining Points (x₁ , y₁) and (x₂ , y₂) is given by :

$\bf{\implies Mid\;point = [(\frac{x_1 + x_2}{2})\;,(\frac{y_1 + y_2}{2})]}$

$\bf{\implies Mid\;point\;of\;Side(BC) = [(\frac{1 - 3}{2})\;, (\frac{5 - 1}{2})]}$

$\bf{\implies Mid\;point\;of\;Side(BC) = [(\frac{-2}{2})\;, (\frac{4}{2})]}$

$\bf{\implies Mid\;point\;of\;Side(BC) = (-1\;,2)}$

We need to Realize that : The Length of Median through Vertex (A) which is joining the Opposite Side BC is the Distance between the Points of Vertex (A) and the Mid point of Side BC

We know that, Distance between two points (x₁ , y₁) and (x₂ , y₂) is given by :

✿  $\bf{Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}$

The Distance between the Vertex [A] (5 , 1) and Midpoint of the Side BC (-1 , 2) is given by :

$\bf{\implies Distance = \sqrt{(5 + 1)^2 + (1 - 2)^2}}$

$\bf{\implies Distance = \sqrt{(6)^2 + (-1)^2}}$

$\bf{\implies Distance = \sqrt{36 + 1}}$

$\bf{\implies Distance = \sqrt{37}}$

$\bf{\implies Length\;of\;the\;Median\;through\;Vertex\;(A)\;is\;\sqrt{37}}$