Answer:
WO ![\sqrt{13}\ \ \ \frac{3}{2}](https://tex.z-dn.net/?f=%5Csqrt%7B13%7D%5C%20%5C%20%5C%20%20%5Cfrac%7B3%7D%7B2%7D)
OR ![\sqrt{13}\ \ \ - \frac{3}{2}](https://tex.z-dn.net/?f=%5Csqrt%7B13%7D%5C%20%5C%20%5C%20-%20%5Cfrac%7B3%7D%7B2%7D)
RM ![\sqrt{13}\ \ \ \frac{3}{2}](https://tex.z-dn.net/?f=%5Csqrt%7B13%7D%5C%20%5C%20%5C%20%20%5Cfrac%7B3%7D%7B2%7D)
MW ![\sqrt{13}\ \ \ - \frac{3}{2}](https://tex.z-dn.net/?f=%5Csqrt%7B13%7D%5C%20%5C%20%5C%20-%20%5Cfrac%7B3%7D%7B2%7D)
Step-by-step explanation:
One has to find the slope, and the distance between the successive points on the plane. Use the slope and distance formula to achieve this.
Slope formula:
![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Distance formula:
![\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_1-x_2%29%5E2%2B%28y_1-y_2%29%5E2%7D)
Remember, the general format for the coordinates of a point on a Cartesian coordinate plane is the following:
![(x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29)
1. WO
Coordinates of point (W): (3, -5)
Coordinates of point (O): (6, -3)
<u>Find the slope:</u>
![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\frac{(-5)-(-3)}{(3)-(6)}=\frac{-5+3}{3-6}=\frac{-2}{-3}=\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B%28-5%29-%28-3%29%7D%7B%283%29-%286%29%7D%3D%5Cfrac%7B-5%2B3%7D%7B3-6%7D%3D%5Cfrac%7B-2%7D%7B-3%7D%3D%5Cfrac%7B2%7D%7B3%7D)
<u>Find the distance:</u>
![\sqrt{((-5)-(-3))^2+((3)-(6))^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28%28-5%29-%28-3%29%29%5E2%2B%28%283%29-%286%29%29%5E2%7D)
![\sqrt{(-2)^2+(-3)^2}\\=\sqrt{4+9}\\=\sqrt{13}\\](https://tex.z-dn.net/?f=%5Csqrt%7B%28-2%29%5E2%2B%28-3%29%5E2%7D%5C%5C%3D%5Csqrt%7B4%2B9%7D%5C%5C%3D%5Csqrt%7B13%7D%5C%5C)
2. OR
Coordinates of point (O): (6, -3)
Coordinates of point (R): (4, 0)
<u>Find the slope:</u>
![\frac{y_2-y_1}{x_2-x_1}\\=\frac{(0)-(-3)}{(4)-(6)}=\frac{3}{-2}=-\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%3D%5Cfrac%7B%280%29-%28-3%29%7D%7B%284%29-%286%29%7D%3D%5Cfrac%7B3%7D%7B-2%7D%3D-%5Cfrac%7B3%7D%7B2%7D)
<u>Find the distance:</u>
![\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
![\sqrt{((0)-(-3))^2+((4)-(6))^2}=\sqrt{(3)^2+(2)^2}=\sqrt{9+4}=\sqrt{13}](https://tex.z-dn.net/?f=%5Csqrt%7B%28%280%29-%28-3%29%29%5E2%2B%28%284%29-%286%29%29%5E2%7D%3D%5Csqrt%7B%283%29%5E2%2B%282%29%5E2%7D%3D%5Csqrt%7B9%2B4%7D%3D%5Csqrt%7B13%7D)
3. RM
Coordinates of point (R): (4, 0)
Coordinates of point (M): (1, -2)
<u>Find the slope:</u>
![\frac{y_2-y_1}{x_2-x_1}\\=\frac{(0)-(-2)}{(4)-(1)}=\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%3D%5Cfrac%7B%280%29-%28-2%29%7D%7B%284%29-%281%29%7D%3D%5Cfrac%7B2%7D%7B3%7D)
<u>Find the distance:</u>
![\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
![\sqrt{((-2)-(0))^2+((1)-(4))^2}=\sqrt{(-2)^2+(-3)^2}=\sqrt{4+9}=\sqrt{13}](https://tex.z-dn.net/?f=%5Csqrt%7B%28%28-2%29-%280%29%29%5E2%2B%28%281%29-%284%29%29%5E2%7D%3D%5Csqrt%7B%28-2%29%5E2%2B%28-3%29%5E2%7D%3D%5Csqrt%7B4%2B9%7D%3D%5Csqrt%7B13%7D)
4. MW
Coordinates of point (M): (1, -2)
Coordinates of point (W): (3, -5)
<u>Find the slope:</u>
![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![=\frac{(-5)-(-2)}{(3)-(1)}=\frac{-3}{2}=-\frac{3}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%28-5%29-%28-2%29%7D%7B%283%29-%281%29%7D%3D%5Cfrac%7B-3%7D%7B2%7D%3D-%5Cfrac%7B3%7D%7B2%7D)
<u>Find the distance:</u>
![\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
![=\sqrt{((3)-(1))^2+((-5)-(-2))^2}=\sqrt{(2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%28%283%29-%281%29%29%5E2%2B%28%28-5%29-%28-2%29%29%5E2%7D%3D%5Csqrt%7B%282%29%5E2%2B%283%29%5E2%7D%3D%5Csqrt%7B4%2B9%7D%3D%5Csqrt%7B13%7D)