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 C1 = (-1, 7) and C2 = (-7, 13).
At first, we need to compute the vector distance between A(x,y) = (2,4) and B(x,y) = (-10, 16) by following vectorial subtraction.
AB = B - A ............................1
Where AB is Vector Distance between A and B, Dimensionless.
A, B - Vector distance between each point and origin, dimensionless.
If we know that A(x, y) = (2, 4) and B(x,y) = (-10, 16), then we have the following results:
AB = (-10, 16) - (2, 4)
AB = (-10 -2, 16, -4)
AB = (-12, 12)
Note that we can find the location of an point inside the line segment by using the following vectorial equation:
C = A + r * AB......................2
Where
r - Segment factor, dimensionless.
C- Location of resulting point, dimensionless.
There are two different options for the location of resulting point: r1 = 1/4 and r2 = 3/4 Now we proceed to find each option:
r1 = 1/4
C1 = (2, 4) + 1/4 * (-12, 12)
C1 = (2,4) + (-3, 3)
C1 = (-1, 7)
R2 = 3/4
C2 = (2,4) + 3/4 * (-12,12)
= (-7, 13)
The two points on a stretch connecting the United States Capital and the White House where the ratio of the shorter segments formed by each is 1: 3 are C1 = (-1, 7) and (-7, 13)
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