Question

Let (1,2),(3,6) and (0,4) be the three vertices of triangle. Find the equation of the median through (0,4) and also, find the length of the median​.

Answer 1

The equation of the median through (0,4) is y = 4. The length of the median is 2.

Step-by-step explanation:

The equation of the median through (0,4) can be found by calculating the midpoint of the line segment connecting the other two vertices of the triangle. Let's find the equation step-by-step:

1. Find the midpoint of the line segment connecting (1,2) and (3,6). The midpoint formula is: ((1+3)/2, (2+6)/2) = (2, 4);
2. Find the equation of the line passing through (0,4) and (2,4) using the point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line. Since the slope is 0, the equation becomes y = 4;
3. Hence, the equation of the median through (0,4) is y = 4.

To find the length of the median, we can use the distance formula between (0,4) and (2,4):

d = sqrt((2-0)^2 + (4-4)^2) = sqrt(4) = 2