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.

Answer:

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 [tex]\vec C_{1} =(-1,7)[/tex] and [tex]\vec C_{2} = (-7,13)[/tex].

Step-by-step explanation:

At first we need to calculate the vector distance between [tex]A(x,y) = (2, 4)[/tex] and [tex]B(x,y) =(-10,16)[/tex] by following vectorial subtraction:

[tex]\overrightarrow{AB} = \vec B - \vec A[/tex] (Eq. 1)

Where:

[tex]\overrightarrow{AB}[/tex] - Vector distance between points A and B, dimensionless.

[tex]\vec A[/tex], [tex]\vec B[/tex] - Vector distance between each point and origin, dimensionless.

If we know that [tex]A(x,y) = (2, 4)[/tex] and [tex]B(x,y) =(-10,16)[/tex], then we have the following result:

[tex]\overrightarrow {AB} = (-10,16)-(2,4)[/tex]

[tex]\overrightarrow{AB} = (-10-2,16-4)[/tex]

[tex]\overrightarrow{AB} = (-12,12)[/tex]

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

[tex]\vec C = \vec A + r\cdot \overrightarrow{AB}[/tex] (Eq. 2)

Where:

[tex]r[/tex] - Segment factor, dimensionless.

[tex]\vec C[/tex] - Location of resulting point, dimensionless.

There are two different options for the location of resulting point: [tex]r_{1} = \frac{1}{4}[/tex] and [tex]r_{2} = \frac{3}{4}[/tex]. Now we proceed to find each option:

[tex]r_{1} = \frac{1}{4}[/tex]

[tex]\vec C_{1} = (2,4) +\frac{1}{4}\cdot (-12,12)[/tex]

[tex]\vec C_{1} = (2,4)+(-3,3)[/tex]

[tex]\vec C_{1} =(-1,7)[/tex]

[tex]r_{2} = \frac{3}{4}[/tex]

[tex]\vec C_{2} = (2,4) +\frac{3}{4}\cdot (-12,12)[/tex]

[tex]\vec C_{2} = (2,4) +(-9,9)[/tex]

[tex]\vec C_{2} = (-7,13)[/tex]

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 [tex]\vec C_{1} =(-1,7)[/tex] and [tex]\vec C_{2} = (-7,13)[/tex].

Jacob split the cost of snacks, which was $12.24, with two friends. Before they ate, another friend joined them and paid Jacob for his fourth of the cost.
How much does Jacob need to refund each of the other two friends so that everyone pays the same amount?

3(4x - 2) > 7x + 19

The graph represents the relationship between the cost of renting a trailer y for x hours,, please help

What is angle KNL

Enter your answer in the box
[]

-3a + b when a
=
-4 and b = 9.

2(4+c)=67 help solve for c

The volume of the box is modeled by the function V (x) = 5x^2 + 5x. What is the volume when x= 4?
А-120 cubic units
B-30 cubic units
C-100 cubic units
D-45 cubic units

Tristan and two of his friends purchased tickets to a school play. Tristan paid for all the tickets with a $50.00 bill and received $23.00 in change. If Tristan used a coupon for 25% off, what was the original price for one ticket?

Which point is a solution to the inequality shown in this graph?


A (6,0)

B (5,-5)

C (0,-3)

D (0,-5)

Can someone please answer this question for me 3(7q−10)

I totally need help, (I just wanna see who will join)
It works :)
kte-diym-hvy

A student is working two jobs over the summer to pay for a new car. The student gets paid $25 for each lawn that
is mowed ( 2 )and $15 for each pool that is cleaned (y). The student wants to earn $750 to pay for a down payment
on a car.


•What is the y-intercept

John has 125 marbles. 35 are green; 40 are red; 20 are yellow and the rest are blue. What is the ratio of the blue marbles to all the marbles? *

40 to 30
6 to 25
25 to 6
35 to 125

Find the y-intercept in the function: 3x - 2y = 6*​

I need help please 20 points

1. (01.01 LC)
Which of the following is a rational number? (5 points)
√2, √3. √4. √5.

Help me. 1,2,3, and 4 are the only options for all letters so there is no lack of information in this picture.

HEY CAN ANYONE PLS ANSWER DIS MATH QUESTION!!!!!!!!!!

What is 6+6+2
need to actually ask something to give away points or the bots will report lol

which of the following explains why soft drinks are such an unhealthy choice?

A. one soft drink contains about 25% of daily caloric intake

B. one soft drink contains nearly an entire daily allowance for sugar

C. the carbonation contains unnatural additives that contribute to obesity

D. the carbonation is a preservatives that also adds sugar ​

Pleaseee help me with my math show work please I need the work

on the number line between two consecutive whole numbers would square root of 7 be located at

Which cube is formed by folding the pattern?​

Melissa collects data on her college graduating class. She finds out that of her classmates,40%are brunettes ,30%have blue eyes and 5% are brunettes that have blue eyes. What is the probability that one of melissa's classmates will be a brunette or have blue eyes?

definition of congruence: if

Suppose that R and S are points on the number line. If RS=9 and R lies at -6 where could S be located

Select all that apply
Which of the following name a line in the drawing ?

In one month, Jillian made 36 local phone calls and 20 long distance calls.

What was her ratio of local calls to long distance calls for that month?


A. 2:1

B. 3:2

C. 9:4

D. 9:5

Solve for the indicated variable.



A = LW, solve for W

Anne owns a used car lot and in order to get cars to sell, she buys used cars at an
auction place. It costs $200 to attend the auction and she buys used cars at
$2,000 each. Last Tuesday, she purchased 10 cars. Which of the following
functions correctly represents this situation in function notation?
f(x) = 10x + 200
f(x) = 200x + 2,000
f(x) = 2,000x + 10
f(x) = 2,000x + 200