A) DaQuan marks two points on the coordinate plane. One point is L(4, 2) and the other point is

M(7, 6). What is the correct way for DaQuan to set up the distance formula? (1 point)
d = √(6 − 7)
2 + (2 − 4)
2
d = √(2 − 4)
2 + (6 − 7)
2
d = √(2 − 7)
2 + (4 − 6)
2
d = √(4 − 7)
2 + (2 − 6)

1 answer

The distance formula for two points \( L(x_1, y_1) \) and \( M(x_2, y_2) \) in the coordinate plane is given by:

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

For the points \( L(4, 2) \) and \( M(7, 6) \), we identify:

  • \( (x_1, y_1) = (4, 2) \)
  • \( (x_2, y_2) = (7, 6) \)

Plugging the coordinates into the distance formula, we have:

\[ d = \sqrt{(6 - 2)^2 + (7 - 4)^2} \]

This translates to:

\[ d = \sqrt{(2)^2 + (3)^2} \]

Now let's analyze the options provided:

  1. d = √(6 − 7)² + (2 − 4)² - This is incorrect, as the coordinates are mixed up.
  2. d = √(2 − 4)² + (6 − 7)² - This is incorrect as well, for similar reasons.
  3. d = √(2 − 7)² + (4 − 6)² - This is incorrect, as this swaps the points.
  4. d = √(4 − 7)² + (2 − 6)² - This is the correct formula where \( x_1 = 4 \), \( x_2 = 7 \) and \( y_1 = 2 \), \( y_2 = 6 \).

Thus, the correct option for how DaQuan should set up the distance formula is:

d = √(4 − 7)² + (2 − 6)²