To find the distance between two points \( M = (-7, 9) \) and \( J = (-4, 1) \) in the coordinate plane, we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, we can identify the coordinates:
- \( M(x_1, y_1) = (-7, 9) \)
- \( J(x_2, y_2) = (-4, 1) \)
Now plug in the coordinates into the distance formula:
\[ d = \sqrt{((-4) - (-7))^2 + (1 - 9)^2} \]
Calculating each part step-by-step:
-
Calculate \( x_2 - x_1 \): \[ -4 - (-7) = -4 + 7 = 3 \]
-
Calculate \( y_2 - y_1 \): \[ 1 - 9 = -8 \]
Now, square each result:
\[ d = \sqrt{(3)^2 + (-8)^2} \]
Calculating the squares:
\[ d = \sqrt{9 + 64} \]
Now, add these values:
\[ d = \sqrt{73} \]
Thus, the exact distance between the points \( M \) and \( J \) is:
\[ \boxed{\sqrt{73}} \]