Question

The co-ordinates of the vertices of ΔABC are A(3, 1), B(1, 6) and C(5, 4). The length of median through A is ______.

Options

• 7

• 6

• 5

• 4

Answer 1

The co-ordinates of the vertices of ΔABC are A(3, 1), B(1, 6) and C(5, 4). The length of median through A is 4.

Explanation:

Midpoint of BC:

= `((1 + 5)/2, (6 + 4)/2)`

= (3, 5)

Median from A goes to this midpoint;

AM = `sqrt[(3-3)^2 + (5-1)^2]`

AM = `sqrt(16)`

∴ AM = 4

Because the x-coordinates match, the median is vertical, and its length equals the y-difference of 4.