Given a line segment with endpoints a(16, 8) and b(1, 3) what are the coordinates of the line segment partitioned two-fifths from a to b?

The coordinates of the line segment partitioned two-fifths from A to B is; (82/7, 46/7)

We are given the coordinates of the line segment AB as;

A(16, 8) and B(1, 3)

Since the partition is 2/5 from A to B, then it means that the point that divides AB into 2/5 has the coordinates;

X-coordinate of P = (mx2 + nx1)/(m + n)

Y-coordinate of P = (my2 + ny1)/(m + n)

Where;

m and n are the ratios of the division.

Thus, m = 2 and n = 5

X-coordinate = ((2 × 1) + (5 × 16))/(2 + 5)

X-coordinate = (2 + 80)/7

X - coordinate = 82/7

Y-coordinate = ((2 × 3) + (5 × 8))/(2 + 5)

Y-coordinate = (6 + 40)/7

Y-coordinate = 46/7

Read more about division of line into segments at; link

Check the picture below.

since it's being cut in 2/5 thus a ratio of 2:5, which means that AB is being cut into 2+5 or 7 even pieces, AP takes 2 of those and PB takes 5 of those.

Also notice that "from A to B" matters greatly, since that means AP takes the smaller ratio, whilst the other takes the other, let's check then,

In the first triangle 80+20+p=180 (since sum of all angles of a triangle is 180)so p= 80also in second triangle 55+45+q=180 (since sum of all angles of a triangle is 180)so q=80so we can conclude that p=80 degrees q=80 degrees so p=q=80 degreeshence option b is correct

10feet apart then both