5. On a street map of his town, Jordan's house has coordinates $$ (8,1) $$. The town's two high schools are at $$ (0,5) $$ and $$ (6,11) $$. a) Which school is closer to Jordan's house?

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To determine which high school is closer to Jordan's house, we can calculate the distance from Jordan's house at coordinates $$ (8,1) $$ to each of the high schools at coordinates $$ (0,5) $$ and $$ (6,11) $$ using the distance formula:

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

### Distance to the first high school at $$ (0,5) $$:

Let $$ (x_1, y_1) = (8, 1) $$ and $$ (x_2, y_2) = (0, 5) $$.

$$
d_1 = \sqrt{(0 - 8)^2 + (5 - 1)^2}
$$
$$
d_1 = \sqrt{(-8)^2 + (4)^2}
$$
$$
d_1 = \sqrt{64 + 16}
$$
$$
d_1 = \sqrt{80}
$$
$$
d_1 = 4\sqrt{5} \approx 8.94
$$

### Distance to the second high school at $$ (6,11) $$:

Let $$ (x_1, y_1) = (8, 1) $$ and $$ (x_2, y_2) = (6, 11) $$.

$$
d_2 = \sqrt{(6 - 8)^2 + (11 - 1)^2}
$$
$$
d_2 = \sqrt{(-2)^2 + (10)^2}
$$
$$
d_2 = \sqrt{4 + 100}
$$
$$
d_2 = \sqrt{104}
$$
$$
d_2 = 2\sqrt{26} \approx 10.20
$$

### Conclusion:

Now we compare the two distances:

- Distance to the first high school: $$ d_1 \approx 8.94 $$
- Distance to the second high school: $$ d_2 \approx 10.20 $$

Since $$ 8.94 < 10.20 $$, Jordan's house is closer to the first high school at $$ (0,5) $$.
Jordan's house is closer to the first high school at $$ (0,5) $$.

5. On a street map of his town, Jordan's house has coordinates \( (8,1) \). The town's two high schools are at \( (0,5) \) and \( (6,11) \). a) Which school is closer to Jordan's house?

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