Here is my question: If (2, -3) and

(-5, 4 are the endpoints of a diagonal of a square, what are the coordinates of the other two vertices?

I got (2,3) and (-5,-4). But the other question was:

What is the area of the square?

How would you find this? Do you just count the number of tickmarks in between the vertices and then multiply like you would a normal square, or is there another correct way?

Thank you! Any help is appreciated!

You did the hardest part correctly.

Once you have the corner coordinates, square the length of any side to get the area.

The length of the diagonal of your square is sqrt[7^2 + 7^2] = 7 sqrt 2, so the length of sides should be 7.

The area must be 49

Your other points are not correct, a simple case of graphing them would have shown you they don't form a square.

I got (2,4) and (-5,-3) as the other points.

Check: In a square the diagonals are equal and right-bisect each other.

For my points both are equal to 7√2 and their slopes are +1 and -1

the base length is 7, and the height of course is also 7, for an area of 49 square units

Ummm... I did graph them, and why would it be (-5, -3)?

That would make the square... slightly diagonal, wouldn't it. I said -4 because that is directly below 4.

Reiny is correct about the other two point coordinates. I should have used real graph paper, or verified the side lengths. All must be 7.

To find the coordinates of the other two vertices of the square, we need to understand the properties of a square.

In a square, opposite sides are parallel and equal in length, and all four angles are right angles.

So, to find the other two vertices, we need to consider the diagonal line connecting the given endpoints as one of the diagonals of the square.

First, let's find the length of the diagonal. We can use the distance formula between two points to calculate it:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

For the given endpoints, (2, -3) and (-5, 4):

Distance = sqrt((-5 - 2)^2 + (4 - (-3))^2)
= sqrt((-7)^2 + (7)^2)
= sqrt(49 + 49)
= sqrt(98)
= 7 * sqrt(2)

Since a square has diagonals of equal length, the other diagonal is also 7 * sqrt(2).

Now, let's find the coordinates of the other two vertices:

1. Start with one endpoint (let's say (2, -3)) and add the diagonal length to both x and y coordinates. This will give us one vertex.

Vertex 1: (2 + 7 * sqrt(2), -3 + 7 * sqrt(2))
= (2 + 7 * sqrt(2), -3 + 7 * sqrt(2))

2. Start with the other endpoint (let's say (-5, 4)) and subtract the diagonal length from both x and y coordinates. This will give us the other vertex.

Vertex 2: (-5 - 7 * sqrt(2), 4 - 7 * sqrt(2))
= (-5 - 7 * sqrt(2), 4 - 7 * sqrt(2))

So, the coordinates of the other two vertices are:
Vertex 1: (2 + 7 * sqrt(2), -3 + 7 * sqrt(2))
Vertex 2: (-5 - 7 * sqrt(2), 4 - 7 * sqrt(2))

To find the area of the square, we can use the distance formula again. Since a square has equal sides, we just need to find the length of one side.

We know that the diagonal length is 7 * sqrt(2). To find the side length, we can divide the diagonal length by sqrt(2) since the diagonal divides the square into two congruent right-angled triangles.

Side length = (Diagonal length) / sqrt(2)
= 7 * sqrt(2) / sqrt(2)
= 7

Now, we can calculate the area of the square by squaring the length of one side:

Area = (Side length)^2
= (7)^2
= 49 square units

So, the area of the square is 49 square units.

To summarize:
- The coordinates of the other two vertices are:
Vertex 1: (2 + 7 * sqrt(2), -3 + 7 * sqrt(2))
Vertex 2: (-5 - 7 * sqrt(2), 4 - 7 * sqrt(2))

- The area of the square is 49 square units.