Geometry
given triangle def with d(-4, -1), e(-1, 8), and f(5,4), find the median dt in point-slope form

 
y-6 = (7/6)(x-2)



Explanation:

The median DT goes from point D, which is given, to point T which we have to find. The point T is the midpoint of segment EF.

Use the midpoint formula to find the midpoint. Add up the x coordinates of E and F to get
-1+5 = 4
Then divide that by 2
4/2 = 2
The x coordinate of point T is x = 2

Repeat for the y coordinates
8+4 = 12
12/2 = 6
The y coordinate of point T is y = 6

So the point T is (x,y) = (2,6)



We know point D is (-4,-1)
We just found point T to be (2,6)

Using the slope formula, the slope is..
m = (y2-y1)/(x2-x1)
m = (6-(-1))/(2-(-4))
m = (6+1)/(2+4)
m = 7/6
The slope is m = 7/6

Use either the coordinates of D or T. I'll use point T. So (x1,y1) = (2,6) meaning x1 = 2 and y1 = 6

We'll plug m = 7/6, x1 = 2 and y1 = 6 into the point slope equation
y-y1 = m(x-x1)
y-6 = (7/6)(x-2)

which is the final answer