To find the distance [tex]\( d \)[/tex] between the points [tex]\( A = (2, 5) \)[/tex] and [tex]\( B = (-6, -3) \)[/tex], we will use the distance formula. The distance formula is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Here, the coordinates are:
- [tex]\( x_1 = 2 \)[/tex]
- [tex]\( y_1 = 5 \)[/tex]
- [tex]\( x_2 = -6 \)[/tex]
- [tex]\( y_2 = -3 \)[/tex]
Let's follow these steps to calculate the distance:
1. Find the difference between the x-coordinates:
[tex]\[ x_2 - x_1 = -6 - 2 = -8 \][/tex]
2. Find the difference between the y-coordinates:
[tex]\[ y_2 - y_1 = -3 - 5 = -8 \][/tex]
3. Square these differences:
[tex]\[ (x_2 - x_1)^2 = (-8)^2 = 64 \][/tex]
[tex]\[ (y_2 - y_1)^2 = (-8)^2 = 64 \][/tex]
4. Add the squares:
[tex]\[ (x_2 - x_1)^2 + (y_2 - y_1)^2 = 64 + 64 = 128 \][/tex]
5. Take the square root of the sum:
[tex]\[ d = \sqrt{128} \approx 11.3137 \][/tex]
6. Round to the nearest tenth:
[tex]\[ d \approx 11.3 \][/tex]
So, the distance [tex]\( d \)[/tex] between points [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is approximately 11.3 units.
