What are the coordinates of the point on the directed line segment from (-8, -2) to (6,2) that partitions the segment into a ratio of 1 to 3?

The coordinates of the point are (-4.5,-1).

Step-by-step explanation:

We want to find point T(x,y).

I am going to say that out points are A(-8,-2) and B(6,2)

Since it partitions the segment in a 1:3 ratio, we have that:.

We apply this to both the x-coordinate and y-coordinate of T.

x-coordinate:

x-coordinate of A: -8

x-coordinate of B: 6

x-coordinate of T: x.

So

y-coordinate:

y-coordinate of A: -2

y-coordinate of B: 2

y-coordinate of T: y.

The coordinates of the point are (-4.5,-1).

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

283 square feet

step-by-step explanation:

good luck