Triangle ABC has the coordinates A (3,4), B (-5,2), C (1, -4). If point E is the midpoint of BC, find the equation of the median which goes through points A and

Question

Triangle ABC has the coordinates A (3,4), B (-5,2), C (1, -4). If point E is the midpoint of BC, find the equation of the median which goes through points A and E. 

 

Answer 1

We need to find the midpoint E. So we start by taking to coordinates of B and C, add the respective x and ys and divide by 2:

 

X coordinate: -5 + 1 = -4   -4 / 2 = -2

Y coordinate: 2 + -4 = -2   -2 / 2 = -1

E = (-2, -1)

 

Now to find the slope between A and E:

^{4 - (-1)} / _{3 - (-2)} → ^{4 + 1}/_{3 + 2} = ⁵/₅  = 1

so the slope = 1

 

To find b, we can look at point E and note that the x-coordinate is at -2, so we add 2 to both the x and y coordinates to see where it crosses the y-axis:

 

(-2, -1) + (2, 2) = (0, 1)

So the b = 1

y = mx + b, and now we have slope and b for a line going through points A and E:

y = x + 1