Question

Can someone please help me ?

Answer 1

The coordinate of B is (3, 7).

Solution:

Given data: A(0, 6), D(18, 12) and AB : BD = 1 : 5

A(0, 6) can be taken as $A(x_1, y_1)$.

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

AB : BD can be taken as m : n = 1 : 5.

We know that coordinate of point P(x, y) divides line segment joining

$(x_1, y_1)$ and $(x_2, y_2)$ in ratio m : n is

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

Here, $x_1=0, x_2=18, y_1=6, y_2=12$ and m = 1, n = 5.

Substitute these in the above formula, we get

$B(x,y)=(\frac{1(18)+5(0)}{1+5}, \frac{1(12)+5(6)}{1+5})$

⇒ $B(x,y)=(\frac{18+0}{6}, \frac{12+30)}{6})$

⇒ $B(x,y)=(\frac{18}{6}, \frac{42}{6})$

⇒ B(x, y) = (3, 7)

Hence the coordinates of point B are (3, 7).