Question
If the vertices of a square are A(−1,4), B(−6,4), C(−6,−1), and D(−1,−1), how long is each side?(1 point)
Answers
GPT 3.5
The distance between two points in a coordinate plane is calculated using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Using this formula, we can calculate the lengths of the sides of the square:
1. Length of side AB:
\[ AB = \sqrt{((-6) - (-1))^2 + (4 - 4)^2} = \sqrt{(5^2 + 0^2)} = \sqrt{25} = 5 \]
2. Length of side BC:
\[ BC = \sqrt{((-6) - (-6))^2 + ((-1) - 4)^2} = \sqrt{(0^2 + (-5)^2)} = \sqrt{25} = 5 \]
3. Length of side CD:
\[ CD = \sqrt{((-1) - (-6))^2 + ((-1) - (-1))^2} = \sqrt{(5^2 + 0^2)} = \sqrt{25} = 5 \]
4. Length of side DA:
\[ DA = \sqrt{((-1) - (-1))^2 + (4 - (-1))^2} = \sqrt{(0^2 + 5^2)} = \sqrt{25} = 5 \]
Therefore, each side of the square has a length of 5 units.
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Using this formula, we can calculate the lengths of the sides of the square:
1. Length of side AB:
\[ AB = \sqrt{((-6) - (-1))^2 + (4 - 4)^2} = \sqrt{(5^2 + 0^2)} = \sqrt{25} = 5 \]
2. Length of side BC:
\[ BC = \sqrt{((-6) - (-6))^2 + ((-1) - 4)^2} = \sqrt{(0^2 + (-5)^2)} = \sqrt{25} = 5 \]
3. Length of side CD:
\[ CD = \sqrt{((-1) - (-6))^2 + ((-1) - (-1))^2} = \sqrt{(5^2 + 0^2)} = \sqrt{25} = 5 \]
4. Length of side DA:
\[ DA = \sqrt{((-1) - (-1))^2 + (4 - (-1))^2} = \sqrt{(0^2 + 5^2)} = \sqrt{25} = 5 \]
Therefore, each side of the square has a length of 5 units.