To find the distance between two points on a grid, we can use the distance formula. Given two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], the distance [tex]\(d\)[/tex] between them is given by the formula:
[tex]\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\][/tex]
Let's determine the coordinates of the two points:
- Point 1: [tex]\((-4, -5)\)[/tex]
- Point 2: [tex]\((-1, -10)\)[/tex]
Next, we need to calculate the differences in the x-coordinates and y-coordinates:
- The difference in the x-coordinates ([tex]\(\Delta x\)[/tex]) is calculated as follows:
[tex]\[
\Delta x = x_2 - x_1 = -1 - (-4) = -1 + 4 = 3
\][/tex]
- The difference in the y-coordinates ([tex]\(\Delta y\)[/tex]) is calculated as follows:
[tex]\[
\Delta y = y_2 - y_1 = -10 - (-5) = -10 + 5 = -5
\][/tex]
Now, substitute these differences into the distance formula:
[tex]\[
d = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{(3)^2 + (-5)^2} = \sqrt{9 + 25} = \sqrt{34}
\][/tex]
Thus, the distance between the two points is:
[tex]\[
d = \sqrt{34} \approx 5.83
\][/tex]
So, the differences in the coordinates are [tex]\(\Delta x = 3\)[/tex] and [tex]\(\Delta y = -5\)[/tex], and the distance between the points [tex]\((-4, -5)\)[/tex] and [tex]\((-1, -10)\)[/tex] is approximately 5.83 units.
