To find the distance between two points, we can use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points. In this case, the points are \((-8, 10)\) and \((-5, 7)\).
Let's designate:
- \((x_1, y_1) = (-8, 10)\)
- \((x_2, y_2) = (-5, 7)\)
Now, we can apply the distance formula:
\[ d = \sqrt{((-5) - (-8))^2 + ((7) - (10))^2} \]
Calculating the differences:
- \(x_2 - x_1 = -5 + 8 = 3\)
- \(y_2 - y_1 = 7 - 10 = -3\)
Now plug these values into the formula:
\[ d = \sqrt{(3)^2 + (-3)^2} = \sqrt{9 + 9} = \sqrt{18} \]
Next, we simplify \(\sqrt{18}\):
\[ \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2} \]
Calculating \(3\sqrt{2}\):
\[ 3 \times \sqrt{2} \approx 3 \times 1.414 \approx 4.242 \]
Rounding to the nearest tenth gives:
\[ d \approx 4.2 \]
Therefore, the distance of Line A is approximately 4.2.
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