Given M (8,1) and P (-4,5), find the coordinates of point O that lies 3/4 of the way on the directed line Segment MP

Answer 1

Not sure what you mean by directed a picture would help

Since the midpoint splits the line segment in two equal segments, half way down either of resulting halves is 3/4 down the original line

Find the midpoint of M (8,1) and P (-4,5) first

Find the midpoint of the distance between the midpoint and P

Midpoint formula

((x₁+x₂)/2, (y₁+y₂)/2)

(8 +(-4))/2 = (8-4)/2 = 4/2= 2 =x

(1 + 5)/2 = 6/2 = 3 =y

Midpoint of MP is (2,3)

Now we need the midpoint of (2,3) and P(-4,5)

(-4 + 2)/2 = -2/2 = -1 = x

(5 + 3)/2 = 8/2 = 4 = y

3/4 the way (-1,4) for point O between the midpoint and P

You can draw the line and check the point

It is also noticeable that the slope is -1/3 (5 -1)/(-4-8) = 4/-12 = -1/3