The United States Capitol is located at (2, 4) on a coordinate grid. The White

House is located at (-10, 16) on the same coordinate

grid. Find two different points on a segment joining

the United States Capital and the White House such

that the ratio of the two shorter segments created by

each point is 1:3.

The two different point on a segment joining the United States Capital and the White House such that the ratio of the shorter segments created by each is 1 : 3 are and .

Step-by-step explanation:

At first we need to calculate the vector distance between and by following vectorial subtraction:

(Eq. 1)

Where:

- Vector distance between points A and B, dimensionless.

, - Vector distance between each point and origin, dimensionless.

If we know that and , then we have the following result:

Besides, we can find the location of any point inside the line segment by using the following vectorial equation:

(Eq. 2)

Where:

- Segment factor, dimensionless.

- Location of resulting point, dimensionless.

There are two different options for the location of resulting point: and . Now we proceed to find each option:

The two different point on a segment joining the United States Capital and the White House such that the ratio of the shorter segments created by each is 1 : 3 are and .

b. would be the answer : )

step-by-step explanation:

step 1: add -16x to both sides.

16x−4y+−16x=64+−16x  

−4y=−16x+64

step 2: divide both sides by -4.

−4y /-4 = -16x + 64/-4

answer:   y=4x−16

hope i'm right

1. 523.33 cubic inches

2. 113.04 cubic inches.

3. 17.41.

4. 16.49

i think this should be your answer

hope i

-lavira : )