Question

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 points on the straight line between the United States Capitol and the White House such that the ratio is 1:3.

Answer 1

The two different points on a segment joining the United States Capital and the White House such that the ratio of the vector distance created by each is 1 : 3 are C1 = (-1, 7) and C2= (-7, 13)

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

Where:

- Vector distance between points A and B, dimensionless.

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

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

AB= (-10, 16)- (2,4)

AB = (-10-2,16-4)

AB = (-12, 12)

Where:

- Segment factor, dimensionless.

- Location of resulting point, dimensionless.

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

Ci -(2.4)+(-12,12)

Ci =(2,4)+ (-3,3)

C= (-1,7)

ra-3/4

Ca =(2,4)+:(-12, 12)

Ca= (2,4) + (-9,9)

Ca=(-7, 13)

In mathematics and physics, a vector is a term that colloquially refers to a quantity, or element of a vector space, a single number cannot represent that.

Learn more about vector here: brainly.com/question/25705666

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