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).

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.