So the closest point is \( \left( \frac{4}{25}, \frac{78}{25} \right) \).

February 22, 2026

$So the closest point is \( \left( \frac{4}{25}, \frac{78}{25} \right) \).$

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9x + 16x - 40 + 36 = 0 \Rightarrow 25x - 4 = 0 \Rightarrow x = \frac{4}{25}
Now find \( y \):
y = -\frac{4}{3} \cdot \frac{4}{25} + \frac{10}{3} = -\frac{16}{75} + \frac{250}{75} = \frac{234}{75} = \frac{78}{25}
Alternatively, use the formula for projection. The distance from point \( (x_0, y_0) \) to line \( ax + by + c = 0 \) is not what we want — we want the **point**. But the vector projection method confirms.
answer is the point:
\boxed{\left( \frac{4}{25}, \frac{78}{25} \right)}

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