Question

the coordinates of the endpoints of $overline{bc}$ are $b(-10, -7)$ and $c(0, -2)$. point $d$ is on $bc$ and divides it such that $bd:cd$ is $3:2$. what are the coordinates of $d$? write your answers as integers or decimals.

Explanation:

Step1: Use the section - formula for x - coordinate

The section formula for the x - coordinate of a point \(D(x,y)\) that divides the line segment joining \(B(x_1,y_1)\) and \(C(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(x_1=-10\), \(x_2 = 0\), \(m = 3\), \(n = 2\).
\[x=\frac{3\times0+2\times(-10)}{3 + 2}=\frac{0-20}{5}=-4\]

Step2: Use the section - formula for y - coordinate

The section formula for the y - coordinate of a point \(D(x,y)\) that divides the line segment joining \(B(x_1,y_1)\) and \(C(x_2,y_2)\) in the ratio \(m:n\) is \(y=\frac{my_2+ny_1}{m + n}\). Here, \(y_1=-7\), \(y_2=-2\), \(m = 3\), \(n = 2\).
\[y=\frac{3\times(-2)+2\times(-7)}{3 + 2}=\frac{-6-14}{5}=\frac{-20}{5}=-4\]

Answer:

\((-4,-4)\)