Question

The point S is on the line AB so that lengths AS:SB are in the ration 3:2. If A = (21,3) and B = (6, 33) then find the co ordinate of S

Answer 1

From the section formula, it was found that the coordinate for the point S is (12,21).

Section Formula

The coordinates of the point S which divides the line AB into two sections can be found from the application of the Section Formula that is presented below:

$S=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})$, where

$ratio=\frac{m}{n}$

$x_1$ and $y_1$ are coordinates of A

$x_2$ and $y_2$ are coordinates of  B

• Find the point S

The question gives  r=$\frac{3}{2}$, A=(21,3) and B=(6,33). From the ratio, you can find m=3 and n=2.

Next step, applying the internal section formula. Then, you have:

$S=(\frac{3*6+2*21}{3+2}, \frac{3*33+2*3}{3+2})\\ \\ S=(\frac{18+42}{5}, \frac{99+6}{5})\\ \\ S=(\frac{60}{5}, \frac{105}{5})\\ \\ S=(12, 21)$

Read more about the section formula here:

brainly.com/question/14812336

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