Find the distance between the two points. $$ (x, y)=(-17,-2) \text { and }(x, y)=(-1,7) $$ $$ \square $$ Additional Materials

Question

UpStudy AI · Accepted Answer

We start by using the distance formula for two points $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$, which is given by

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

Given the points $$ (-17,-2) $$ and $$ (-1,7) $$, we identify

$$
x_1 = -17, \quad y_1 = -2, \quad x_2 = -1, \quad y_2 = 7.
$$

1. Compute the difference in the $$ x $$-coordinates:

$$
x_2 - x_1 = -1 - (-17) = -1 + 17 = 16.
$$

2. Compute the difference in the $$ y $$-coordinates:

$$
y_2 - y_1 = 7 - (-2) = 7 + 2 = 9.
$$

3. Square each difference:

$$
(16)^2 = 256, \quad (9)^2 = 81.
$$

4. Sum the squared differences:

$$
256 + 81 = 337.
$$

5. Take the square root to find the distance:

$$
d = \sqrt{337}.
$$

Thus, the distance between the given points is

$$
\boxed{\sqrt{337}}.
$$
The distance between the points $$(-17, -2)$$ and $$(-1, 7)$$ is $$\sqrt{337}$$.

Find the distance between the two points. \[ (x, y)=(-17,-2) \text { and }(x, y)=(-1,7) \] \( \square \) Additional Materials