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Point A is at (6, 1) and point C is at (2, - 7).
Find the coordinates of point Bon AC such that AB
= {BC.

Answer 1

The coordinates of the point B on AC is (5, -1)

How to determine the coordinates of the point B on AC

From the question, we have the following parameters that can be used in our computation:

A is at (6, 1) and point C is at (2, - 7).

And we have the partition to be

m : n = 1 : 3

The coordinate of the partition is calculated as

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

Substitute the known values in the above equation, so, we have the following representation

B = 1/4 * (1 * 2 + 3 * 6, 1 * -7 + 3 * 1)

Evaluate

B = 1/4 * (20, -4)

So, we have

B = (5, -1)

Hence, the coordinates of the point B on AC is (5, -1)

Question

Point A is at (6,1) and point C is at (2,-7) find the coordinates of point B on AC such that AB = 1/3BC

Answer 2

Answer: (4, -3)

Explanation:

The Midpoint is the point equidistant from AB and BC.

Use the Midpoint formula:

`M_x=(x_1+x_2)/(2)\qquad \qquad \qquad M_y=(y_1+y_2)/(2)\\\\\\M_x=(6+2)/(2)\qquad \qquad \qquad \quad M_y=(1-7)/(2)\\\\\\M_x=(8)/(2)\qquad \qquad \qquad \qquad \quad M_y=(-6)/(2)\\\\\\M_x=4\qquad \qquad \qquad \qquad \quad M_y=-3`

(4, -3)