Respuesta :
Answer:
Therefore 2/3 of (-2,9) to (5,-1) = [tex]\frac{2}{3} \times \sqrt{149}[/tex] = 8.138
Step-by-step explanation:
i) the given two points [tex](x_{1} , y_{1})[/tex] and [tex](x_{2} , y_{2})[/tex] are given as (-2, 9) and (5,-1) respectively.
ii) the given section mentioned above is to be divided in the ratio 2/3.
iii) the formula to find the point (x, y) which divides a line segment in the ratio m:n is given by
x = [tex]\dfrac{mx_{2} + nx_{1}}{m + n}[/tex] = [tex]\frac{(2 \times 5) + (3 \times -2) }{2 + 3}[/tex] = [tex]\frac{4}{5}[/tex] and y = [tex]\dfrac{my_{2} + ny_{1}}{m + n}[/tex]= [tex]\frac{(2 \times -1) + (3 \times 9) }{2 + 3}[/tex] = 5
iv) The distance between the two points [tex](x_{1} , y_{1})[/tex] and [tex](x_{2} , y_{2})[/tex] are given as (-2, 9) and (5,-1) = [tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}} = \sqrt{(5 - (-2))^{2} + (-1 - 9)^{2}} = \sqrt{7^{2} + (-10)^{2} } = \sqrt{49 + 100} = \sqrt{149}[/tex]v) Therefore 2/3 of (-2,9) to (5,-1) = [tex]\frac{2}{3} \times \sqrt{149}[/tex] = 8.138
