Glad of their custom and wishing them well, the ski-boat manager makes special arrangements for Mel and her husband to do a final-evening tandem waterski run at sunset, straight from the harbour mouth to the lighthouse and back. Treating their course from point (2,4) to (9,6) as the hypotenuse of a right-angled triangle, how far - to the nearest whole metre - do they go in this single run?




To find the distance Mel and her husband travel during their tandem waterski run, we can treat the course from point \((2, 4)\) to \((9, 6)\) as the hypotenuse of a right-angled triangle.

We can use the **distance formula**, which is derived from the Pythagorean theorem:

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

Given points:
- Point 1: \((2, 4)\)
- Point 2: \((9, 6)\)

### Step 1: Plug in the coordinates into the distance formula.

\[
\text{Distance} = \sqrt{(9 - 2)^2 + (6 - 4)^2}
\]

### Step 2: Calculate the differences.

\[
\text{Distance} = \sqrt{7^2 + 2^2}
\]
\[
\text{Distance} = \sqrt{49 + 4}
\]
\[
\text{Distance} = \sqrt{53}
\]

### Step 3: Find the square root of 53.
Now, calculate the square root of 53 and round it to the nearest whole number.

Let me calculate that for you.The distance Mel and her husband travel during their tandem waterski run is approximately **7 metres**, rounded to the nearest whole metre.

Would you like to delve deeper into any part of this? Here are some related questions:

1. How would the distance change if the lighthouse were at a different point?
2. What is the exact value of the distance without rounding?
3. How much longer would the run be if they started from the point (0,0)?
4. What if the return trip from the lighthouse were along a different path?
5. Could you use trigonometry to find the angle they ski along?

**Tip:** The distance formula is a practical application of the Pythagorean theorem, useful for finding straight-line distances in a coordinate plane.

Learn how to calculate the distance traveled during a tandem waterski run using the Pythagorean theorem and distance formula. Solve the problem of determining the straight-line distance between two points on a coordinate plane. Suitable for students in Grades 7-9.

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