Question

You can use the Pythagorean Theorem to find the area of a square when you know its end points.

A square garden has the end points listed below. Plot and label these points on the grid:
A (−7, 6)B (−2, −6)C (10, −1)D (5, 11)

Connect the points to create Square ABCD
.
Use the Pythagorean Theorem to find the side length, s
, of Square ABCD
.
Use the area formula, A = s2
, to find the area of Square ABCD
.

Answer 1

To plot and label the points on the grid, you can do the following:

1. Create a coordinate grid on a piece of paper or a graphing program.
2. Mark the x-axis and y-axis.
3. Plot point A at (-7, 6).
4. Plot point B at (-2, -6).
5. Plot point C at (10, -1).
6. Plot point D at (5, 11).
7. Draw lines to connect the points A, B, C, and D, forming a square ABCD.

To find the side length (s) of Square ABCD using the Pythagorean Theorem, you can use the following formula:

s^2 = (x2 - x1)^2 + (y2 - y1)^2

where (x1, y1) and (x2, y2) are the coordinates of two points on the same side of the square.

Let's find the side length using the coordinates of points A and B:

s^2 = (-2 - (-7))^2 + (-6 - 6)^2
= (5)^2 + (-12)^2
= 25 + 144
= 169

Taking the square root of both sides, we get:

s = √169
= 13

Therefore, the side length of Square ABCD is 13 units.

To find the area of Square ABCD, you can use the formula A = s^2, where s is the side length:

A = (13)^2
= 169

Therefore, the area of Square ABCD is 169 square units.