Question

the distance between the points l(7, -1) and m(-2, 4). answer in simplest exact fo... exact distance between the two points is box.

Explanation:

Step1: Recall the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
For points \( L(7, -1) \) and \( M(-2, 4) \), we have \( x_1 = 7 \), \( y_1 = -1 \), \( x_2 = -2 \), \( y_2 = 4 \).

Step2: Substitute values into the formula

First, calculate \( x_2 - x_1 \) and \( y_2 - y_1 \):
\( x_2 - x_1 = -2 - 7 = -9 \)
\( y_2 - y_1 = 4 - (-1) = 4 + 1 = 5 \)

Then, substitute these into the distance formula:
\( d = \sqrt{(-9)^2 + 5^2} \)

Step3: Simplify the expression

Calculate the squares:
\( (-9)^2 = 81 \)
\( 5^2 = 25 \)

Add the results:
\( 81 + 25 = 106 \)

So, \( d = \sqrt{106} \)

Answer:

\(\sqrt{106}\)