What are the coordinates of the point 3/5 of the way from A(-9,3) to B(21,-2)

Answer:  The required co-ordinates of the point are (9, 0). Step-by-step explanation:  We are given to find the co-ordinates of the point that is [tex]\dfrac{3}{5}[/tex] of the way from A(-9,3) to B(21, -2).Let K be the required point. Then, we mus have[tex]AK:AB=3:5\\\\\Rightarrow \dfrac{AK}{AK+BK}=\dfrac{3}{5}\\\\\\\Rightarrow 5AK=3AK+3BK\\\\\Rightarrow 2AK=3BK\\\\\Rightarrow AK:BK=3:2.[/tex]We know thatthe co-ordinates of a point that divides the line joining the points (a, b) and (c, d) in the ratio m : n are given by[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{2}\right).[/tex]For the given division, m : n = 3 : 2.Therefore, the co-ordinates of the point K are[tex]\left(\dfrac{3\times21+2\times(-9)}{3+2},\dfrac{3\times(-2)+2\times3}{3+2}\right)\\\\\\=\left(\dfrac{63-18}{5},\dfrac{-6+6}{5}\right)\\\\=\left(\dfrac{45}{5},\dfrac{0}{5}\right)\\\\=(9,0).[/tex]Thus, the required co-ordinates of the point are (9, 0).