Asked by fish

Guided Practice

Type your answer and then click or tap Done.

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

Answers

Answered by GPT-4o
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.
There are no human answers yet. A form for humans to post answers is coming very soon!

Related Questions