What is the distance between point P (primates) and point C (cats) on the map?

Steps to Solve

1. Identify the coordinates of points P and C

   By observing the graph, we note the positions of the points:

   • Point $P$ (primate) is located at the coordinates $(-2, 1)$.
   • Point $C$ (cat) is located at the coordinates $(8, -1)$.

2. Use the distance formula

   The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated using the formula: $$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

3. Substitute the coordinates into the distance formula

   Plugging in the coordinates of points $P$ and $C$:

   • $x_1 = -2$, $y_1 = 1$
   • $x_2 = 8$, $y_2 = -1$

   Thus, we have: $$ d = \sqrt{(8 - (-2))^2 + (-1 - 1)^2} $$

4. Calculate the differences and squares

   Simplifying the expressions:

   • $8 - (-2) = 8 + 2 = 10$
   • $-1 - 1 = -2$

   Therefore, we rewrite the equation: $$ d = \sqrt{10^2 + (-2)^2} $$

5. Calculate the squares

   Now we compute the squares:

   • $10^2 = 100$
   • $(-2)^2 = 4$

   This gives us: $$ d = \sqrt{100 + 4} $$

6. Find the final value of distance

   Finally, calculating the root: $$ d = \sqrt{104} $$ This can further be simplified: $$ d = 2\sqrt{26} $$