Question

What would be the coordinate of point P which divides the line joining A(-4,1) and B (17,10) in the ratio 1:2?

Answer 1

Here, the line segment is divided into 3 equal parts means trisection.
This can be done by finding two points P and Q on the line segment AB , AP = PQ= QB.
Let AP = PQ= QB = X
AP = X & PB = PQ +QB = x +x = 2x
AP : PB = x : 2x = 1:2
AQ=AP + PQ = x + x = 2x & QB =X
AQ : QB = 2x : x = 2 :1
Hence,P divides the line segment AB in the ratio 1:2 & Q divide the line segment AB in the ratio 2:1.
SOLUTION IS IN THE ATTACHMENT.

HOPE THIS WILL HELP YOU....

Answer 2

● Coordinate geometry ●

A(- 4 , 1) and B(17, 10)

P divides AB in 1 : 2 ratio.

Coordinates of P =

$x \: coordinate = \frac{1 \times 17 + 2 \times ( - 4)}{1 + 2} \\ \\ = \frac{17 - 8}{3} \\ \\ = \frac{9}{3} \\ \\ = 3$


And ,

$y \: coordinate = \frac{1 \times 10 + 2 \times 1}{1 + 2} \\ \\ = \frac{10 + 2}{3} \\ \\ = \frac{12}{3} \\ \\ = 4$


Therefore, coordinates of P = ( 3, 4).