Question

DaQuan marks two points on the coordinate plane. One point is L (4,2) and the other is M (7,6). What is the correct way for DaQuan to set up the distance formula?

a. d = √ (6 - 7^2 + (2 - 4)^2
b. d = √ (2 - 7)^2 + (4 - 6)^2
c. d = √ (4 - 7)^2 + (2 - 6)^2
d. d = √ (2 - 4)^2 + (6 - 7)^2

Answer 1

The distance formula to find the distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) in the coordinate plane is given by:

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

Given the points L (4, 2) and M (7, 6), we can identify:
- \( (x_1, y_1) = (4, 2) \)
- \( (x_2, y_2) = (7, 6) \)

We will substitute these values into the distance formula:

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

Calculating this:

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

Thus:

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

Now, let's check the options provided:

a. \( d = \sqrt{(6 - 7)^2 + (2 - 4)^2} \) (incorrect values)
b. \( d = \sqrt{(2 - 7)^2 + (4 - 6)^2} \) (incorrect values)
c. \( d = \sqrt{(4 - 7)^2 + (2 - 6)^2} \) (this is correct: \(d = \sqrt{(-3)^2 + (-4)^2}\))
d. \( d = \sqrt{(2 - 4)^2 + (6 - 7)^2} \) (incorrect values)

The correct option is:

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