Question

alex marks two points on the coordinate plane. one point is a(4, 1) and the other point is b(-1, 5). what is the correct way for alex to set up the distance formula? (1 point)
( circ d=sqrt{(1 - 4)^{2}+(5 - 1)^{2}} )
( circ d=sqrt{(4 - 1)^{2}+(5 - 1)^{2}} )
( circ d=sqrt{(-1 - 4)^{2}+(1 - -5)^{2}} )
( circ d=sqrt{(-1 - 4)^{2}+(5 - 1)^{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

Here, \(x_1 = 4,y_1=1,x_2=-1,y_2 = 5\).

Step3: Substitute into the formula

Substitute the values into the formula: \(d=\sqrt{(-1 - 4)^2+(5 - 1)^2}\).

Answer:

\(d=\sqrt{(-1 - 4)^2+(5 - 1)^2}\) (the fourth option)