A, b, and c are collinear, and b is between a and c. the ratio of ab is 1: 1. if a is at (1,-9) and b is at (2,0), what are the coordinates of point c

(3,9)

Step-by-step explanation:

So I drew a right triangle with the line segment A(1,-9) to C as the hypotenuse.  This line segment does contain point B(2,0). This is shown in the picture.

We want to find a point C so that AB to BC has a ratio of 1:1. So this means B is the midpoint really.

So if we averaged the endpoints of the line segment it would equate to point B.

That is:

and

Multiply both sides by 2:

and

The first equation can be solved by subtracting 1 on both sides giving .

The second equation can be solved by adding 9 on both sides giving

.

Point C is (3,9).

the distance from any point on the parabola to the focus is the exact same as the distance from that point to the directrix.

if you could provide answer choices that might allow me to answer the question easier if my above answer isn't an option! (:

1350 hats

step-by-step explanation:

divide 900 by 2 to find 50% or half of 900

900/2=450

add 450 to 900

1350