Question

Given x(4,1) and b(8,9), find a if the ratio of ax to xb is 1:2. your answer should be written as an ordered pair and decimal, no fractions.

Answer 1

The coordinates of point a is (-2, 6)

How to determine a in the ratio ax to xb?

The points are given as:

x = (4, 1)

b = (8, 9)

m : n = 1 : 2

The coordinates of x are calculated as:

x = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have:

(4, 1) = 1/(1 + 2) * (8 + 2x, 9 + y)

This gives

(4, 1) = 1/3 * (8 + 2x, 9 + y)

Multiply by 3

(12, 3) = (8 + 2x, 9 + y)

Solve for x and y

2x + 8 = 12

y + 9 = 3

This gives

x = -2

y = -6

Hence, the coordinates of point a is (-2, 6)

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