Question

1. directed line segment wg has endpoints at w(-3,3) and g(6,-3). directed line segment wg is partitioned ⅔ of the distance from w to g at point d.

a. what is the horizontal distance of wd?
b. what is the vertical distance of wd?
c. what are the coordinates of point d?

Explanation:

Step1: Calculate horizontal distance between W and G

The formula for horizontal distance (change in x - values) between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $\Delta x=x_2 - x_1$. Here, $x_1=-3$ (x - coordinate of W) and $x_2 = 6$ (x - coordinate of G), so $\Delta x=6-(-3)=9$. The horizontal distance of WD is $\frac{2}{3}$ of this value. So, $9\times\frac{2}{3}=6$.

Step2: Calculate vertical distance between W and G

The formula for vertical distance (change in y - values) between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $\Delta y=y_2 - y_1$. Here, $y_1 = 3$ (y - coordinate of W) and $y_2=-3$ (y - coordinate of G), so $\Delta y=-3 - 3=-6$. The vertical distance of WD is $\frac{2}{3}$ of this value. So, $-6\times\frac{2}{3}=-4$.

Step3: Find coordinates of point D

The coordinates of a point that divides a line - segment from $(x_1,y_1)$ to $(x_2,y_2)$ in the ratio $m:n$ are given by $x=x_1+\frac{m}{m + n}(x_2 - x_1)$ and $y=y_1+\frac{m}{m + n}(y_2 - y_1)$. Here, $m = 2$, $n = 1$, $x_1=-3$, $y_1 = 3$. $x=-3+6 = 3$, $y=3+( - 4)=-1$.

Answer:

a. 6
b. -4
c. (3,-1)