Question

distance in the coordinate plane quick check
daijuan 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 daijuan to set up the distance formula? (1 point)
( d=sqrt{(2 - 4)^{2}+(6 - 7)^{2}} )
( d=sqrt{(4 - 7)^{2}+(2 - 6)^{2}} )
( d=sqrt{(2 - 7)^{2}+(4 - 6)^{2}} )
( d=sqrt{(4 - 7)^{2}+(2 - 6)^{2}} )

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Identify the coordinates

For points \(L(4,2)\) (\(x_1 = 4,y_1=2\)) and \(M(7,0)\) (\(x_2 = 7,y_2 = 0\)).

Step3: Substitute into the formula

Substitute into the formula: \(d=\sqrt{(7 - 4)^2+(0 - 2)^2}\) which is equivalent to \(d=\sqrt{(4 - 7)^2+(2 - 0)^2}\) (since \((a - b)^2=(b - a)^2\)).

Answer:

\(d=\sqrt{(4 - 7)^2+(2 - 0)^2}\) (the fourth option in the given choices)