Question

The vertices of triangle are A(3,4), B(2,0) and C(-1,6) Find equation of median through vertex A ​

Answer 1

Answer:

2x-5y+14 = 0

Step-by-step explanation:

A median is a line drawn from the vertex of a triangle joining the midpoint of opposite side.

A median also passes through the centroid of the triangle.

Denoting A as (x1,y1) , B as (x2,y2) and C as (x3,y3)

First, we find the centroid G(a,b) using formula

a = (x1 +x2 +x3 ) / 3 = (3+2+(-1) )/3 = 4/3

b = (y1 +y2+ y3 ) /3 = (4+0+6) /3 = 10/3

So, the coordinates G(a,b) are (4/3,10/3)

Now, to find the equation of median (which passes through A and G) , we will first calculate the slope.

slope = (y3 - b) / ( x3 - a) = 2/5

Using slope-point form, equation will be

slope = (y - y1) / (x-x1)

implies, 2/5 = y-4 / x-3

cross-multiplying, we get

2x -6 = 5y -20

implies, 2x -5y +14 = 0

This is the required equation of the median.