Question

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

Answer 1

WO
`√(13)\ \ \ (3)/(2)`

OR
`√(13)\ \ \ - (3)/(2)`

RM
`√(13)\ \ \ (3)/(2)`

MW
`√(13)\ \ \ - (3)/(2)`

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:

`(y_2-y_1)/(x_2-x_1)`

Distance formula:

`√((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:

`(y_2-y_1)/(x_2-x_1)`

`((-5)-(-3))/((3)-(6))=(-5+3)/(3-6)=(-2)/(-3)=(2)/(3)`

Find the distance:

`√(((-5)-(-3))^2+((3)-(6))^2)`

`√((-2)^2+(-3)^2)\\=√(4+9)\\=√(13)\\`

2. OR

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

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

Find the slope:

`(y_2-y_1)/(x_2-x_1)\\=((0)-(-3))/((4)-(6))=(3)/(-2)=-(3)/(2)`

Find the distance:

`√((x_2-x_1)^2+(y_2-y_1)^2)`

`√(((0)-(-3))^2+((4)-(6))^2)=√((3)^2+(2)^2)=√(9+4)=√(13)`

3. RM

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

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

Find the slope:

`(y_2-y_1)/(x_2-x_1)\\=((0)-(-2))/((4)-(1))=(2)/(3)`

Find the distance:

`√((x_2-x_1)^2+(y_2-y_1)^2)`

`√(((-2)-(0))^2+((1)-(4))^2)=√((-2)^2+(-3)^2)=√(4+9)=√(13)`

4. MW

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

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

Find the slope:

`(y_2-y_1)/(x_2-x_1)`

`=((-5)-(-2))/((3)-(1))=(-3)/(2)=-(3)/(2)`

Find the distance:

`√((x_2-x_1)^2+(y_2-y_1)^2)`

`=√(((3)-(1))^2+((-5)-(-2))^2)=√((2)^2+(3)^2)=√(4+9)=√(13)`