Question

What is the equation of the median from vertex X for the triangle with vertices X(1,−2),Y(7,4), and Z(8,−7)?

A. y−2=0
B. x−8y−16=0
C. x−7y−15=0
D. (x - 13y - 2 = 0)

Answer 1

The equation of the median from vertex X for the given triangle is x - 7y - 15 = 0.

Step-by-step explanation:

To find the equation of the median from vertex X, we need to find the midpoint of the side YZ. To find the midpoint, we add the x-coordinates of Y and Z and divide by 2, and add the y-coordinates of Y and Z and divide by 2.

The x-coordinate of the midpoint is (7 + 8) / 2 = 15 / 2,

and the y-coordinate of the midpoint is (4 + -7) / 2 = -3 / 2.

Therefore, the equation of the median from vertex X is the equation of the line passing through X(1, -2) and the midpoint (15/2, -3/2). Using the point-slope form, the equation is:

y - (-2) = (1 - (15/2))/(15/2) * (x - 1)

Simplifying, we get x - 7y - 15 = 0.