Question

select the coordinates of point x on ab that is ⅕ of the distance from a to b. a) (3.6, -2.2) b) (-3.6, 2.2) c) (-3.6, -2.2) d) (3.6, 2.2) a(-5, -5) b(2, 9)

Explanation:

Step1: Recall the section - formula

If a point \(X(x,y)\) divides the line - segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(m = 1\), \(n=4\), \(x_1=-5\), \(y_1=-5\), \(x_2 = 2\), and \(y_2=9\).

Step2: Calculate the x - coordinate of point X

\[x=\frac{1\times2+4\times(-5)}{1 + 4}=\frac{2-20}{5}=\frac{-18}{5}=-3.6\]

Step3: Calculate the y - coordinate of point X

\[y=\frac{1\times9+4\times(-5)}{1 + 4}=\frac{9-20}{5}=\frac{-11}{5}=-2.2\]

Answer:

C. \((-3.6,-2.2)\)