Question

What are the coordinates of point C on the directed segment from A (-8,4) to B (10,2) that partitions the segment such that AC:CB is 2:1?

Answer 1

Answer:

(14/3, 8/3)

Step-by-step explanation:

Let the points be

$(x_1,y_1) = A(-8,4)\\(x_2,y_2) = B(10,2)$

The formula for finding the coordinates of point that divides the line in a:b is:

$x = \frac{bx_1+ax_2}{a+b} \\y = \frac{by_1+ay_2}{a+b}$

Here x and y are the coordinates of the point that will partition the line into given ratios

Our ratio is 2 to 1,

So,

a=2

b=1

Putting the values in the formula

$x = \frac{(1)(-8)+(2)(10)}{2+1}\\x = \frac{-8+20}{3}\\x =\frac{14}{3}\\y = \frac{(1)(4)+(2)(2)}{3}\\y=\frac{4+4}{3} \\y= \frac{8}{3}$

So the coordinates of point that divides AB in 2:1 are:

(14/3, 8/3) ..

Answer 2

Answer:

The correct point is (14/3,8/3)