Question

A parallelogram has vertices J(-3,9), K(3,9), L(1,1), and M(-5,1).

Show opposite sides are congruent by using the distance formula

Answer 1

Using the distance formula;
`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

We find the length of each side of the parallelogram as follows:

Side JK

`|JK|=√((3--3)^2+(9-9)^2)`

`|JK|=√((3+3)^2+(0)^2)`

`|JK|=√((6)^2+(0)^2)`

`|JK|=√((6)^2+(0)^2)`

`|JK|=√((6)^2+0)`

`|JK|=√((6)^2)`

`|JK|=√((6)^2)=6` units

Side KL

`|KL|=√((1-3)^2+(1-9)^2)`

`|KL|=√((-2)^2+(-8)^2)`

`|KL|=√(4+64)`

`|KL|=√(68)`

`|KL|=8.25` units

Side LM

`|LM|=√((-5-1)^2+(1-1)^2)`

`|LM|=√((-6)^2+(0)^2)`

`|LM|=√(36)`

`|LM|=6` units

Side MJ

`|MJ|=√((-3--5)^2+(9-1)^2)`

`|MJ|=√((-3+5)^2+(9-1)^2)`

`|MJ|=√((2)^2+(8)^2)`

`|MJ|=√(4+64)`

`|MJ|=√(68)`

`|MJ|=8.25` units.

We can see that

`|JK|=|ML|=6` units

`|MJ|=|LK|=8.25` units .

Since the opposite sides are equal, they are congruent.

See diagram