Let $(x_A,y_A),\ (x_B,y_B)$ be the coordinates of the points A and B and $(x_0,y_0)$ be the coordinates of the point O that divides the segment AB in ratio 2:3.

Consider vectors

$\overrightarrow{AO}=(x_0-x_A,y_0-y_A),\\ \\\overrightarrow{OB}=(x_B-x_0,y_B-y_0).$

These vectors are collinear and

$\dfrac{\overrightarrow{AO}}{\overrightarrow{OB}}=\dfrac{2}{3}.$

Then

$\left\{\begin{array}{l}\dfrac{x_0-x_A}{x_B-x_0}=\dfrac{2}{3}\\ \\\dfrac{y_0-y_A}{y_B-y_0}=\dfrac{2}{3}\end{array}\right.\Rightarrow \left\{\begin{array}{l}3(x_0-x_A)=2(x_B-x_0)\\ \\3(y_0-y_A)=2(y_B-y_0)\end{array}\right..$

This means that

$\left\{\begin{array}{l}3x_0-3x_A=2x_B-2x_0\\ \\3y_0-3y_A=2y_B-2y_0\end{array}\right.\Rightarrow \left\{\begin{array}{l}5x_0=2x_B+3x_A\\ \\5y_0=2y_B+3y_A\end{array}\right..$

Thus,

$x_0=\dfrac{2x_B+3x_A}{5},\ y_0=\dfrac{2y_B+3y_A}{5}.$

Answer: $\left(\dfrac{2x_B+3x_A}{5},\dfrac{2y_B+3y_A}{5}\right).$

8 0

4 years ago

Read 2 more answers

I go to a baseball field and survey the people in the stands, asking what is your favorite sport. Is this a fair sample of peopl

Alinara [238K]

Answer:

No.

Step-by-step explanation:

If you go to a baseball park and ask what their favorite sport is most will probably say baseball. Just as if you go to a basketball court, most would respond with basketball as their favorite sport. I suggest not going to anything related to sports and asking random people.

4 0

3 years ago

2 < X < 8<br> x is an integer.<br> Write down the possible values of x.

Rufina [12.5K]

answer: 3, 4, 5, 6, 7

4 0

3 years ago

An automobile has a price of $16,000 after being discounted 20%. what is the original price?

stepan [7]

<span>$16,000 / (100% - 20%) = $16,000 / .8 = $20,000
to verify, work the answer backwards.
$20,000 - $20,000 * 20% = $20,000 - $4,000 = $16,000
</span>

6 0

3 years ago