Question : If A(-2, 2), B(1, -1) and C (5,1) are the vertices of triangle ABC, find the length of the median through the vertex A?
Doubt by Vanshika
Solution :
We know,
Median of a triangle from a vertex to the opposite side of the triangle divide the opposite side in two equal parts.
Let
A (-2, 2)
B (1, -1)
A (-2, 2)
B (1, -1)
C (5, 1)
D is the Mid point of BC.
So by Mid Point Formula, we can find the coordinates of D
So by Mid Point Formula, we can find the coordinates of D
D(x4,y4) = [(x2+x3)/2, (y2+y3)/2]
D(x4,y4) = [(1+5)/2, (-1+1)/2]
D(x4,y4) = [6/2, 0/2]
D(x4,y4) = [3,0]
D(x4,y4) = [(1+5)/2, (-1+1)/2]
D(x4,y4) = [6/2, 0/2]
D(x4,y4) = [3,0]
Now by using distance formula, we can find the length of the median AD
AD = √[(x4-x1)2+(y4-y1)2]
AD = √[(3+2)2+(0-2)2]
AD = √[(x4-x1)2+(y4-y1)2]
AD = √[(3+2)2+(0-2)2]
AD = √[25+4]
AD = √29 units
Hence, Required length of the median is √29 units.
AD = √29 units
Hence, Required length of the median is √29 units.