Question

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Find the distance between points A(2, 3) and B(5, 9). Round to the nearest tenth.

Answer 1

To find the distance between two points \( A(2, 3) \) and \( B(5, 9) \), we use the distance formula:

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

Here, the coordinates are:
- \( x_1 = 2 \)
- \( y_1 = 3 \)
- \( x_2 = 5 \)
- \( y_2 = 9 \)

Plugging these values into the formula, we get:

\[ \text{Distance} = \sqrt{(5 - 2)^2 + (9 - 3)^2} \]
\[ \text{Distance} = \sqrt{3^2 + 6^2} \]
\[ \text{Distance} = \sqrt{9 + 36} \]
\[ \text{Distance} = \sqrt{45} \]
\[ \text{Distance} = \sqrt{9 \times 5} \]
\[ \text{Distance} = \sqrt{9} \times \sqrt{5} \]
\[ \text{Distance} = 3 \sqrt{5} \]

Now, we approximate \( \sqrt{5} \):

\[ \sqrt{5} \approx 2.236 \]

Thus,

\[ \text{Distance} \approx 3 \times 2.236 \]
\[ \text{Distance} \approx 6.708 \]

Rounded to the nearest tenth, the distance between points A and B is approximately:

\[ \text{Distance} \approx 6.7 \]

So, the distance between points A(2, 3) and B(5, 9) is approximately 6.7 units.