Question

#12 r(4,-9), s(-7, -2)

Explanation:

Assuming the problem is to find the distance between points \( R(4, -9) \) and \( S(-7, -2) \), we use the distance formula.

Step 1: Recall the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Here, \( x_1 = 4 \), \( y_1 = -9 \), \( x_2 = -7 \), \( y_2 = -2 \).

Step 2: Substitute the values into the formula

First, calculate \( x_2 - x_1 \) and \( y_2 - y_1 \):
\( x_2 - x_1 = -7 - 4 = -11 \)
\( y_2 - y_1 = -2 - (-9) = -2 + 9 = 7 \)

Step 3: Square the differences

\( (-11)^2 = 121 \)
\( 7^2 = 49 \)

Step 4: Sum the squares

\( 121 + 49 = 170 \)

Step 5: Take the square root

\( d = \sqrt{170} \) (or approximately \( 13.04 \) if a decimal approximation is needed)

Answer:

The distance between \( R \) and \( S \) is \( \sqrt{170} \) (or approximately \( 13.04 \)).