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Question Number 54025 by pieroo last updated on 28/Jan/19

$$\mathrm{The}\mathrm{points}\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D}\mathrm{have}\mathrm{coordinates}$$$$(-7,9),(3,4),(1,12),\mathrm{and}(-2,-9).$$$$\mathrm{find}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{linePQ}\mathrm{where}\mathrm{P}$$$$\mathrm{devides}\mathrm{AB}\mathrm{in}\mathrm{the}\mathrm{ratio}2:3\mathrm{and}\mathrm{devides}$$$$\mathrm{CD}\mathrm{in}\mathrm{the}\mathrm{ratio}1:-4.$$

Commented by pieroo last updated on 28/Jan/19

$$\mathrm{I}\mathrm{need}\mathrm{some}\mathrm{help},\mathrm{especially}\mathrm{with}\mathrm{the}$$$$\mathrm{diagram}.$$

Answered by ajfour last updated on 28/Jan/19

Commented by ajfour last updated on 28/Jan/19

$$x_P=\frac{{mx}_B+{nx}_A}{m+n}=\frac{2\left(3\right)+3(-7)}{5}=-3$$$$y_P=\frac{{my}_B+{ny}_A}{m+n}=\frac{2\left(4\right)+3\left(9\right)}{5}=7$$$$P(-3,7)$$$$x_Q=\frac{1(-2)+(-4)\left(1\right)}{-3}=2$$$$y_Q=\frac{1(-9)+(-4)\left(12\right)}{-3}=19$$$$Q(2,19)$$$$PQ=\sqrt{{(-3-2)}^2+{(7-19)}^2}$$$$=\sqrt{25+144}=13units.$$

Commented by pieroo last updated on 28/Jan/19

$$\mathrm{thanks}\mathrm{senior}$$

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