Question

Let a = (-5, 2) and b = (19, 9). find coordinates for the point p between a and b that is three fifths of the way from a to

Answer 1

In this question we need to use ratio formula which is

$( \frac{k_{1} x_{2} +k_{2}x_{1}}{k_{1}+k_{2}} , \frac{k_{1} y_{2} +k_{2}y_{1}}{k_{1}+k_{2}} )$

a .Here

$k_{1}:k_{2}= 3/5:2/5=3:2, x_{1} =-5 , x_{2} =19 , y_{1}=2 , y_{2}=9$

So the required point is

$p = (\frac{3*19+2*(-5)}{3+2},\frac{3*9+2*2}{3+2} )$

$p =(\frac{47}{5},\frac{31}{5} )$

b.And for point q,

$k_{1}:k_{2}= 3:2, x_{1} =19 , x_{2} =-5 , y_{1}=9 , y_{2}=2$

Substituting these values in the formula, we will get

$q =(\frac{3*(-5)+2*(19)}{3+2} , \frac{3*2+2*9}{3+2} )$

$q =(\frac{23}{5},\frac{24}{5})$