Question

I also need to show calculations for each side length plz help

Answer 1

Answer:

WO $\sqrt{13}\ \ \ \frac{3}{2}$

OR $\sqrt{13}\ \ \ - \frac{3}{2}$

RM $\sqrt{13}\ \ \ \frac{3}{2}$

MW $\sqrt{13}\ \ \ - \frac{3}{2}$

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:

$\frac{y_2-y_1}{x_2-x_1}$

Distance formula:

$\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Remember, the general format for the coordinates of a point on a Cartesian coordinate plane is the following:

$(x,y)$

1. WO

Coordinates of point (W): (3, -5)

Coordinates of point (O): (6, -3)

Find the slope:

$\frac{y_2-y_1}{x_2-x_1}$

$\frac{(-5)-(-3)}{(3)-(6)}=\frac{-5+3}{3-6}=\frac{-2}{-3}=\frac{2}{3}$

Find the distance:

$\sqrt{((-5)-(-3))^2+((3)-(6))^2}$

$\sqrt{(-2)^2+(-3)^2}\\=\sqrt{4+9}\\=\sqrt{13}$

2. OR

Coordinates of point (O): (6, -3)

Coordinates of point (R): (4, 0)

Find the slope:

$\frac{y_2-y_1}{x_2-x_1}\\=\frac{(0)-(-3)}{(4)-(6)}=\frac{3}{-2}=-\frac{3}{2}$

Find the distance:

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\sqrt{((0)-(-3))^2+((4)-(6))^2}=\sqrt{(3)^2+(2)^2}=\sqrt{9+4}=\sqrt{13}$

3. RM

Coordinates of point (R): (4, 0)

Coordinates of point (M): (1, -2)

Find the slope:

$\frac{y_2-y_1}{x_2-x_1}\\=\frac{(0)-(-2)}{(4)-(1)}=\frac{2}{3}$

Find the distance:

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\sqrt{((-2)-(0))^2+((1)-(4))^2}=\sqrt{(-2)^2+(-3)^2}=\sqrt{4+9}=\sqrt{13}$

4. MW

Coordinates of point (M): (1, -2)

Coordinates of point (W): (3, -5)

Find the slope:

$\frac{y_2-y_1}{x_2-x_1}$

$=\frac{(-5)-(-2)}{(3)-(1)}=\frac{-3}{2}=-\frac{3}{2}$

Find the distance:

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$=\sqrt{((3)-(1))^2+((-5)-(-2))^2}=\sqrt{(2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}$