Question

point A is located at (2,6) and point B is located at (18,12) . what point partitions the directed line segment ab into a 2:3 ratio

Answer 1

(8.4, 8.4) or $\left(\frac{42}{5}, \frac{42}{5}\right)$

Explanation:

Given points are A(2, 6) and B(18, 12).

Let P(x, y) partitions the line segment in the ratio 2 : 3.

That is AP : PB = 2 : 3.

A(2, 6) can be taken as $A(x_1, y_1).$

B(18, 12) can be taken as $B(x_2, y_2).$

AP : PB can be taken as m : n = 2 : 3.

The coordinate of point P(x, y) divides line segment joining $A(x_1, y_1)$and $B(x_2, y_2)$ in ratio m : n is

$P(x,y)=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})$

Here, $x_1 = 2, x_2=18, y_1=6, y_2=12$ and m = 2, n = 3.

Substitute these in the above formula, we get

$P\left(x, y\right)=\left(\frac{2 \times 18+3 \times 2}{2+3}, \frac{2 \times12+3 \times 6}{2+3}\right)$

           $=\left(\frac{36+6}{5}, \frac{24+18}{5}\right)$

           $=\left(\frac{42}{5}, \frac{42}{5}\right)$

           = (8.4, 8.4)

Hence, the point partitions the line segment is (8.4, 8.4) or $\left(\frac{42}{5}, \frac{42}{5}\right)$.

Answer 2

Answer:

The Correct Answer would be $\frac{42}{5},\frac{42}{5}$ or $8 \frac{2}{5}, 8 \frac{2}{5}$

Step-by-step explanation: