To find the distance between the points (2, -1) and (-1, -5) on the coordinate plane, we can use the Euclidean distance formula. This formula is:
[tex]\[ \text{distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
We need to follow these steps to find the distance:
1. Identify the coordinates of the two points. Let's call the first point [tex]\((x_1, y_1)\)[/tex] and the second point [tex]\((x_2, y_2)\)[/tex]. Here, [tex]\((x_1, y_1) = (2, -1)\)[/tex] and [tex]\((x_2, y_2) = (-1, -5)\)[/tex].
2. Calculate the differences in the x and y coordinates:
- [tex]\( \Delta x = x_2 - x_1 = -1 - 2 = -3 \)[/tex]
- [tex]\( \Delta y = y_2 - y_1 = -5 - (-1) = -5 + 1 = -4 \)[/tex]
3. Substitute these differences into the Euclidean distance formula:
[tex]\[ \text{distance} = \sqrt{(-3)^2 + (-4)^2} \][/tex]
4. Compute the squares of the differences:
- [tex]\((-3)^2 = 9\)[/tex]
- [tex]\((-4)^2 = 16\)[/tex]
5. Add these squared differences:
[tex]\[ 9 + 16 = 25 \][/tex]
6. Take the square root of the sum to find the distance:
[tex]\[ \sqrt{25} = 5 \][/tex]
So, the distance between the points (2, -1) and (-1, -5) on the coordinate plane is 5 units. The correct answer is:
05 units.
