Answer:
The coordinate of point C is (4 , - 6) .
Step-by-step explanation:
Given as ;
The Δ ADC and The Δ DCB are divided in the ratio = m : n = 3 : 4
The coordinate of point A = [tex]x_1 , y _1[/tex] = 1 , - 9
The coordinate of point B = [tex]x_2 , y _2[/tex] = 8 , -2
Let The coordinate of point C = x , y
Now, According to question
x = [tex]\frac{m \times x_2 + n\times x_1}{m + n}[/tex]
Or, x = [tex]\frac{3 \times 8 + 4\times 1}{3 + 4}[/tex]
Or, x = [tex]\frac{24 + 4}{7}[/tex]
∴ x = [tex]\frac{28}{7}[/tex]
i.e x = 4
Similarly
y = [tex]\frac{m \times y_2 + n\times y_1}{m + n}[/tex]
Or, y = [tex]\frac{3 \times (-2) + 4\times (-9)}{3 + 4}[/tex]
Or, y = [tex]\frac{ - 6 - 36}{7}[/tex]
∴ y = [tex]\frac{- 42}{7}[/tex]
i.e y = - 6
So, The coordinate of point C = x , y = 4 , - 6
Hence,The coordinate of point C is (4 , - 6) . Answer
