Question

distance in the coordinate plane quick check
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)
( \bigcirc d = sqrt{(6 - 7)^2 + (2 - 4)^2} )
( \bigcirc d = sqrt{(4 - 7)^2 + (2 - 6)^2} )
( \bigcirc d = sqrt{(2 - 7)^2 + (4 - 6)^2} )
( \bigcirc d = sqrt{(2 - 4)^2 + (6 - 7)^2} )

Explanation:

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) or \(d=\sqrt{(x_1 - x_2)^2+(y_1 - y_2)^2}\) (since squaring eliminates the sign difference).

For points \(L(4,2)\) (so \(x_1 = 4,y_1 = 2\)) and \(M(7,6)\) (so \(x_2 = 7,y_2 = 6\)):

Step 1: Identify \(x_1,y_1,x_2,y_2\)

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

Step 2: Apply distance formula

Using \(d=\sqrt{(x_1 - x_2)^2+(y_1 - y_2)^2}\), substitute the values:
\(d=\sqrt{(4 - 7)^2+(2 - 6)^2}\)

Let's check other options:

• First option: \((6 - 7)^2+(2 - 4)^2\) has incorrect \(y\) and \(x\) differences.
• Third option: \((2 - 7)^2+(4 - 6)^2\) swaps \(x\) and \(y\) coordinates.
• Fourth option: \((2 - 4)^2+(6 - 7)^2\) swaps \(x\) and \(y\) differences incorrectly.

Answer:

\(d=\sqrt{(4 - 7)^2+(2 - 6)^2}\) (the second option among the given choices)