Question

Find the distance of Line A. Round your answer to the nearest tenth.
the codnets are (-8,10) and (-5,7)

Answer 1

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**.