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Answer
If point C divides line AB in the ratio 2:3 the coordinates of C are (3,2)
If point D divides line AC in the ratio 3:2, the coordinates of point D are (2.2,2.8)
Step-by-step explanation:
The coordinates of points C are (4,1).
The coordinates of point D are (3, 2).
Given
The endpoints of AB are A(1,4) and B(6,-1).
What is the formula to find the coordinates?
The formula is used to find the coordinates is;
[tex]\rm x = \dfrac{mx_1+nx_2}{m+n}\\\\y = \dfrac{my_1+my_2}{m+n}[/tex]
If point C divides AB in the ratio 2:3, the coordinates of C are;
[tex]\rm x _c= \dfrac{2(1)+3(6)}{2+3}\\\\\\ x_c= \dfrac{2+18}{5} \\\\ x_c=\dfrac{20}{5}\\\\\rm x_c=4\\\\y_c = \dfrac{2(4)+3(-1)}{2+3}\\\\y_c = \dfrac{8-3}{5}\\\\y_c=\dfrac{5}{5}\\\\y_c=1[/tex]
The coordinates of points C are (4,1).
If point D divides AC in the ratio 3:2, the coordinates of D are;
[tex]\rm x _c= \dfrac{3(1)+2(6)}{3+2}\\\\\\ x_c= \dfrac{3+12}{5} \\\\ x_c=\dfrac{15}{5}\\\\\rm x_c=3\\\\y_c = \dfrac{3(4)+2(-1)}{3+2}\\\\y_c = \dfrac{12-2}{5}\\\\y_c=\dfrac{10}{5}\\\\y_c=2[/tex]
The coordinates of point D are (3, 2).
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