Question

The vertices of a triangle are (2,0) (0,2) (4,6)
then the equation of the median through the
vertex (2,0) is
1) x+y-2=0
2)x=2
3) x+2y-2=0
4) 2x+y-4=0​

Answer 1

Answer:

x=2

....

.....

.....

.........

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Answer 2

The correct option is option (2)

The equation of the median passes through the vertex (2,0) is

x=2

Step-by-step explanation:

Median : A median is a line segment of a triangle. The line segment is formed by joining a vertex to the midpoint of the opposite side.

Given vertices of a triangle is A(2,0), B(0,2) and C(4,6).

The opposite side of the vertex A(2,0) is side BC.

If (x₁,y₁) and (x₂,y₂) are two point.

The co-ordinate of mid point is $=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

x₁=0,y₁=2,x₂=4,y₂=6

The midpoint BC is

$=(\frac{0+4}{2},\frac{2+6}{2})$

=(2,4)

The equation of line passes through point (a₁,b₁) and (a₂,b₂) is

$\therefore (y-a_1)=\frac{b_2-b_1}{a_2-a_1}(x-b_1)$

Here a₁=2,b₁=0, a₂=2,b₂=4

Therefore the required equation of the line is

$(y-0)=\frac{4-0}{2-2}(x-2)$

$\Rightarrow y=\frac{4}{0}(x-2)$

$\Rightarrow x-2=0$

⇒x=2