Question

A(2,3) and B(16, 10) are two points. Find the
co-ordinates of point P on the line segment
AB so that BP: AB = 3:7.​

Answer 1

Answer:

The given question is solved in the uploaded photo.

Answer 2

Answer:

The co-ordinates of the point P is (10 , 7)

$\bf\large\underline{Given}$

• A(2 , 3) and B(16 , 10) are two points . P is such a point on the line segment AB so that BP:AB = 3:7

$\bf\large\underline{To \ Find}$

• The co-ordinates of the point P

$\bf\large\underline{Solution}$

Let the co-ordinates of the point P be (x , y)

We have , A(2 , 3) and B(16 , 10)

Also

$\sf \implies BP : AB = 3:7 \\\\ \sf\implies \dfrac{BP}{AB} = \dfrac{3}{7} \\\\ \sf\implies \dfrac{BP}{AP + BP} = \dfrac{3}{7} \\\\ \sf\implies 3AP + 3BP = 7BP \\\\ \sf\implies 3AP = 4BP \\\\ \sf\implies \dfrac{AP}{BP} = \dfrac{4}{3} \\\\ \sf\implies AP:BP = 4:3$

Thus , from section formula we have :

For X-coordinates :

$\sf \implies x = \dfrac{4 \times 16+ 3 \times 2}{4 + 3} \\ \\ \implies \sf x = \dfrac{64+ 6}{7} \\ \\ \implies \sf x = \dfrac{70}{7} \\ \\ \sf \implies x = 10$

And for Y-coordinates

$\sf \implies y = \dfrac{4 \times 10 + 3 \times 3}{4 + 3} \\ \\ \sf \implies y = \dfrac{40 + 9}{4 + 3} \\ \\ \sf \implies y = \dfrac{49}{7} \\ \\ \sf \implies y = 7$

Thus , the co-ordinates of the point P is (10 , 7)