Question

if A (-2,-2) and B (2,-4) find coordinates of P on AB such that AP = 3/7 AB​

Answer 1

solution:-

co-ordinate of point A and B are (-2,-2) and (2,-4) respectively where,

$AP = \frac{3}{7} AB$

and p is line segment on AB so

AP+BP=AB

$AP + BP = \frac{7}{3} AP$

$BP - \frac{7}{3} AP = AP$

$\frac{AP}{BP} = \frac{3}{4}$

let (x,y) of the coordinate AB is the ration 3:4 internally

so use this formula

$x = \frac{(mx2 + nx1)}{(m + n)}$

and

$y = \frac{(my2 + ny1)}{(m + n)}$

using this formula :- value of x is

$x = \frac{3 \times 2 + (4 \times - 2)}{3 + 4} = \frac{6 - 8}{7} = \frac{ - 2}{7}$

value of y is

$y = \frac{3( - 4) + 4( - 2)}{3 + 4} = \frac{ - 12 - 8}{7} = \frac{ - 20}{7}$

coordinate of point p is

$( \frac{ - 2}{7} , \frac{ - 20}{7} )$

Answer 2

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$( \frac{ - 2}{7} , \frac{ - 20}{7} )$

REFER TO THE ATTACHMENT

Hope it Helps

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