Question

There are coordinates L (-2, 3), M (2, 3), O (-2, -3), and N (2, -3). Find the distance of diagonal LN. Round the answer to the nearest hundredth.

Answer 1

To find the distance of diagonal LN between the points \( L(-2, 3) \) and \( N(2, -3) \), we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

In this case, let:
- \( (x_1, y_1) = (-2, 3) \) (point L)
- \( (x_2, y_2) = (2, -3) \) (point N)

Now plugging the coordinates into the distance formula:

\[
d = \sqrt{(2 - (-2))^2 + (-3 - 3)^2}
\]

Calculating the differences:

\[
x_2 - x_1 = 2 - (-2) = 2 + 2 = 4
\]
\[
y_2 - y_1 = -3 - 3 = -3 - 3 = -6
\]

Now substituting back into the distance formula:

\[
d = \sqrt{(4)^2 + (-6)^2}
\]
\[
d = \sqrt{16 + 36}
\]
\[
d = \sqrt{52}
\]

Next, we can simplify \( \sqrt{52} \):

\[
\sqrt{52} = \sqrt{4 \times 13} = 2\sqrt{13}
\]

Calculating \( 2\sqrt{13} \) using a calculator:

\[
\sqrt{13} \approx 3.60555
\]
\[
2\sqrt{13} \approx 2 \times 3.60555 \approx 7.2111
\]

Now rounding to the nearest hundredth:

\[
d \approx 7.21
\]

Thus, the distance of diagonal LN is approximately **7.21**.