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?

Question

A. d = √(2-4)^2 + (6-7)^2
B. d = √(2-7)^2 + (2-4)^2
C. d = √(6-7)^2 + (2-4)^2
D. d = √(4-7)^2 + (2-6)^2

Answer 1

To find the distance between the points \( L(4, 2) \) and \( M(7, 6) \), we use the distance formula:

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

In this case, \( (x_1, y_1) = (4, 2) \) and \( (x_2, y_2) = (7, 6) \). Plugging in these values into the distance formula, we have:

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

Now let's calculate each part:

1. \( x_2 - x_1 = 7 - 4 = 3 \)
2. \( y_2 - y_1 = 6 - 2 = 4 \)

So, the formula becomes:

\[ d = \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

Now looking at the options:

• A. \( d = \sqrt{(2 - 4)^2 + (6 - 7)^2} \) - Incorrect. (This uses wrong coordinates.)
• B. \( d = \sqrt{(2 - 7)^2 + (2 - 4)^2} \) - Incorrect. (This uses wrong coordinates.)
• C. \( d = \sqrt{(6 - 7)^2 + (2 - 4)^2} \) - Incorrect. (This uses wrong coordinates.)
• D. \( d = \sqrt{(4 - 7)^2 + (2 - 6)^2} \) - Correct. (This is the same distance calculation using the same points but in a slightly different arrangement.)

Thus, the correct answer is:

D. \( d = \sqrt{(4 - 7)^2 + (2 - 6)^2} \)