Question

point p and q trisect the line segment joining the points A -2,0 and B 0,8 such that p is near to 8 find coordinates of point p and q solve it plzzzzz fast

Answer 1

Answer:

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Answer 2

Answer:

Coordinates of P $(\,\frac{-4}{3}\,,\,\frac{8}{3}\,)$  and coordinates of Q $(\,\frac{-2}{3}\,,\,\frac{16}{3}\,)$.

Step-by-step explanation:

Given coordinates of line segment AB where A( -2 , 0 ) and B( 0 , 8 )

           Point P & Q trisect line segment AB

To find: Coordinates of P & Q

Attached Figure.

Since P & Q trisecting the line segment AB

⇒ AP : PQ : QB = 1 : 1 : 1

then

the ratio in which point P intersect AB is 1 : 2

& the ratio in which point Q intersect AB is 2 : 1

let coordinates of P be ( a , b ) and Q be ( l , m )

Now we use Section Formula to coordinate of a point which divide line segment in ration m : n

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

After using this formula we get,

Coordinates of Point P,

$P\,(a,b)\,=\,(\frac{1\times0+2\times(-2)}{1+2},\frac{1\times8+2\times0}{1+2})$  

$P\,(a,b)\,=\,(\frac{-4}{3},\frac{8}{3})$

for Point Q,

$Q\,(l,m)\,=\,(\frac{2\times0+1\times(-2)}{1+2},\frac{2\times8+1\times0}{1+2})$  

$Q\,(l,m)\,=\,(\frac{-2}{3},\frac{16}{3})$

Therefore, Coordinates of P  $(\,\frac{-4}{3}\,,\,\frac{8}{3}\,)$  and coordinates of Q  $(\,\frac{-2}{3}\,,\,\frac{16}{3}\,)$.