Question

Lanna plotted 3 vertacies of a square on a coordinate plane witch are the coordinates of the missing vertext of lanas square

Answer 1

See Explanation

Explanation:

The question is incomplete, as the coordinates of the three vertices.

I will answer your question using the following illustration.

Assume that the square is ABCD are the given coordinates are:

`A = (3,1)`

`B = (-1,5)`

`C = (-5,1)`

Required

Find D

Let the coordinates of D be:

`D = (x,y)`

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Calculate the slope of each side.

AB, BC, CD and DA using:

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

AB:

`A = (3,1)` --
`(x_1,y_1)`

`B = (-1,5)` --
`(x_2,y_2)`

So:

`m_1 = (5 - 1)/(-1 - 3) = (4)/(-4) = -1`

BC:

`B = (-1,5)` --
`(x_1,y_1)`

`C = (-5,1)` --
`(x_2,y_2)`

So:

`m_2 = (1-5)/(-5--1) = (-4)/(-4) = 1`

CD:

`C = (-5,1)` --
`(x_1,y_1)`

`D = (x,y)` --
`(x_2,y_2)`

So:

`m_3 = (y - 1)/(x --5) = (y-1)/(x+5)`

DA

`D = (x,y)` --
`(x_1,y_1)`

`A = (3,1)` --
`(x_2,y_2)`

`m_4 = (1-y)/(3-x)`

AB and CD are parallel sides. So, they have the same slope

i.e.

`m_1 = m_3`

`(y-1)/(x+5) = -1`

Solve:

`y-1 =-x-5`

Make y the subject

`y =-x-5+1`

`y =-x-4` ---- (1)

BC and DA are parallel sides. So, they have the same slope

i.e.

`m_2 = m_4`

`1 = (1-y)/(3-x)`

Solve:

`1-y =3-x`

Make y the subject

`y =1-3+x`

`y =x-2` ---- (2)

So, we have:

`y =-x-4` and
`y =x-2`

Equate both:

`y=y`

`-x-4=x-2`

Collect like terms

`-x-x=4-2`

`-2x=2`

Solve for x

`x = -(2)/(2)`

`x = -1`

Substitute
`x = -1` in
`y =x-2`

`y = -1-2`

`y = -3`

So, the missing coordinate is:

`D = (-1,-3)`