Question

(-1, 4) (-2, -2) 6

Explanation:

Assuming the problem is to find the scale factor or the actual distance between the two points \((-1, 4)\) and \((-2, -2)\) given that a segment of length 6 (maybe on the grid) corresponds to some actual length. First, let's find the distance between the two points using the distance formula.

Step 1: Recall the distance formula

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Here, \((x_1,y_1)=(-1,4)\) and \((x_2,y_2)=(-2,-2)\)

Step 2: Substitute the values into the formula

\(x_2 - x_1=-2-(-1)=-2 + 1=-1\)
\(y_2 - y_1=-2 - 4=-6\)
Then \(d=\sqrt{(-1)^2+(-6)^2}=\sqrt{1 + 36}=\sqrt{37}\approx6.08\)

If we assume that the vertical or horizontal segment of length 6 (from the grid) corresponds to the distance we calculated (approximately 6.08), the scale factor would be approximately \(\frac{6.08}{6}\approx1.01\) (but this is a rough estimate as the problem's grid details are not very clear). If the problem is to find the distance between the two points:

Answer:

The distance between \((-1,4)\) and \((-2,-2)\) is \(\sqrt{37}\approx6.08\)

If the problem was about the scale of the grid (since there is a 6 marked), and we assume that the vertical distance between two horizontal lines (or horizontal distance between two vertical lines) on the grid is related to the 6 units. Let's assume that the vertical distance between the y - coordinates of the two points is \(|4-(-2)| = 6\) and this corresponds to the marked length of 6. So the scale is 1:1 (each unit on the grid is 1 unit in actual length). Then the horizontal distance between the x - coordinates is \(|-1-(-2)|=1\) and vertical distance is 6, so the distance between the two points is \(\sqrt{1^2 + 6^2}=\sqrt{37}\approx6.08\) as before.