Finding the Area of a Garden

Question

Finding the Area of a Garden
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
 .

pls make it sound like an 11 yr old

GPT-4o mini · Answer

**Finding the Area of a Garden** Hey there! Today, we are going to figure out how to find the area of a square garden using some math tricks. First, we have four points that will help us make a square. Here are the points we have: - A (−7, 6) - B (−2, −6) - C (10, −1) - D (5, 11) ### Step 1: Plotting the Points Let’s start by plotting these points on a grid! You can draw a coordinate plane with x (horizontal) and y (vertical) lines: 1. Point A is at (−7, 6). Go to the left 7 and up 6. 2. Point B is at (−2, −6). Go to the left 2 and down 6. 3. Point C is at (10, −1). Go to the right 10 and down 1. 4. Point D is at (5, 11). Go to the right 5 and up 11. After plotting these points, connect them in order to make Square ABCD. ### Step 2: Finding the Side Length, s Now, to find the side length of the square (let's call it "s"), we can use the Pythagorean Theorem, which is a fancy way of saying that in a right triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides. To do this, we need to find the distance between two points. Let’s choose points A and B. We can use the distance formula: $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$ For points A and B: - $ (x_1, y_1) = (-7, 6) $ - $ (x_2, y_2) = (-2, -6) $ Plugging the numbers into the formula: $$ d = \sqrt{((-2) - (-7))^2 + ((-6) - 6)^2} $$ $$ d = \sqrt{(5)^2 + (-12)^2} $$ $$ d = \sqrt{25 + 144} $$ $$ d = \sqrt{169} $$ $$ d = 13 $$ So, the side length $ s $ of Square ABCD is 13. ### Step 3: Finding the Area Finally, we can find the area of the square using the formula: $$ A = s^2 $$ Plugging in our side length: $$ A = 13^2 $$ $$ A = 169 $$ ### Conclusion So, the area of Square ABCD is **169 square units**. Awesome job using the Pythagorean Theorem! Now your garden has a nice area you can plan for! 🌼🌻

puppy · Answer

make it sound like an 11 yr old not a teacher

GPT-4o mini · Answer

**Finding the Area of a Garden** Hey! So today, we’re going to figure out how big a square garden is using some cool math stuff. We have four points to help us make a square. Check out these points: - A (−7, 6) - B (−2, −6) - C (10, −1) - D (5, 11) ### Step 1: Plotting the Points First, let’s draw these points on a grid! Imagine a big graph with two lines crossing each other: 1. For Point A (−7, 6), move left 7 spaces and then up 6. 2. For Point B (−2, −6), go left 2 and down 6. 3. For Point C (10, −1), move right 10 and down 1. 4. For Point D (5, 11), go right 5 and up 11. After you plot them, connect the dots in this order: A, B, C, D, and back to A. Now you should have a cool square! ### Step 2: Finding the Side Length, s Let’s find out how long one side of the square is! We can use the Pythagorean Theorem, which sounds fancy, but it’s just a way to find the distance between two points. We’re going to check the distance between Point A and Point B. Here’s the formula we’ll use: $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$ For A and B: - A is (−7, 6) - B is (−2, −6) Now plug in the numbers: $$ d = \sqrt{((-2) - (-7))^2 + ((-6) - 6)^2} $$ This means: $$ d = \sqrt{(5)^2 + (-12)^2} $$ So now we can figure it out: $$ d = \sqrt{25 + 144} $$ That gives us: $$ d = \sqrt{169} $$ And guess what? $$ d = 13 $$ So, the side length $ s $ of our square is **13**! ### Step 3: Finding the Area Now let's find out how much space that garden takes up. The formula to find the area of a square is: $$ A = s^2 $$ So we just plug in our side length: $$ A = 13^2 $$ That means: $$ A = 169 $$ ### Conclusion So, the area of Square ABCD is **169 square units**! How cool is that? Now you have a super awesome square garden! 🌼🌿

puppy · Answer

MAKE IT SOUND LIKE AN 11 YR OLD TYPED THIS NOT A LESSON PLAN FOR A TEACHER

GPT-4o mini · Answer

**Finding the Area of a Garden!** Hey! 😊 So, I’m trying to find the area of a square garden using these points: - A (−7, 6) - B (−2, −6) - C (10, −1) - D (5, 11) ### Step 1: Plotting the Points First, I’m gonna plot these points on a grid. It’s like making a treasure map! 1. For Point A (−7, 6), I go left 7 and then up 6. That’s A! 2. For Point B (−2, −6), I go left 2 and down 6. There’s B! 3. For Point C (10, −1), I go right 10 and down 1. Yup, that’s C! 4. For Point D (5, 11), I go right 5 and then up 11. D is here! After I plot them, I connect the dots: A to B to C to D and back to A. Now I have a square! ### Step 2: Finding the Side Length, s Now, how long is one side of the square? I’ll use the Pythagorean Theorem (sounds super smart, right?). Let’s find the distance between Point A and Point B. The formula looks like this: $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$ So for A (−7, 6) and B (−2, −6): 1. Plugging in the numbers: - $x_1 = -7$, $y_1 = 6$ - $x_2 = -2$, $y_2 = -6$ 2. Calculate: $$ d = \sqrt{((-2) - (-7))^2 + ((-6) - 6)^2} $$ $$ d = \sqrt{(5)^2 + (-12)^2} $$ $$ d = \sqrt{25 + 144} $$ $$ d = \sqrt{169} $$ $$ d = 13 $$ So, the side length $s$ of the square is **13**! ### Step 3: Finding the Area Alright, now I gotta find the area! The formula is: $$ A = s^2 $$ So I do: $$ A = 13^2 = 169 $$ ### Conclusion So, the area of Square ABCD is **169 square units**! 🎉 Now I know how much space my garden takes up! Isn’t that awesome? 🌼🌿

puppy · Answer

no emojis pls

GPT-4o mini · Answer

**Finding the Area of a Garden** Hey! So, I’m trying to find the area of a square garden using these points: - A (−7, 6) - B (−2, −6) - C (10, −1) - D (5, 11) ### Step 1: Plotting the Points First, I’m going to plot these points on a grid. It’s like making a treasure map! 1. For Point A (−7, 6), I go left 7 and then up 6. That’s A! 2. For Point B (−2, −6), I go left 2 and down 6. There’s B! 3. For Point C (10, −1), I go right 10 and down 1. Yup, that’s C! 4. For Point D (5, 11), I go right 5 and then up 11. D is here! After I plot them, I connect the dots: A to B to C to D and back to A. Now I have a square! ### Step 2: Finding the Side Length, s Now, how long is one side of the square? I’ll use the Pythagorean Theorem. Let’s find the distance between Point A and Point B. The formula looks like this: $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$ So for A (−7, 6) and B (−2, −6): 1. Plugging in the numbers: - $x_1 = -7$, $y_1 = 6$ - $x_2 = -2$, $y_2 = -6$ 2. Calculate: $$ d = \sqrt{((-2) - (-7))^2 + ((-6) - 6)^2} $$ $$ d = \sqrt{(5)^2 + (-12)^2} $$ $$ d = \sqrt{25 + 144} $$ $$ d = \sqrt{169} $$ $$ d = 13 $$ So, the side length $s$ of the square is 13. ### Step 3: Finding the Area Now I need to find the area! The formula is: $$ A = s^2 $$ So I do: $$ A = 13^2 = 169 $$ ### Conclusion So, the area of Square ABCD is 169 square units. Now I know how much space my garden takes up!