Question

what is the distance in the standard (x,y) coordinate plane between the points (0,0) and (3,4)? 2 5 7 12

Explanation:

Step1: Use the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 0,y_1 = 0,x_2=3,y_2 = 4\).

Step2: Substitute the values into the formula

Substitute the values: \(d=\sqrt{(3 - 0)^2+(4 - 0)^2}=\sqrt{3^2+4^2}\).

Step3: Calculate the squares

\(3^2 = 9\) and \(4^2=16\), so \(d=\sqrt{9 + 16}\).

Step4: Add the numbers inside the square root

\(9+16 = 25\), then \(d=\sqrt{25}\).

Step5: Simplify the square root

\(\sqrt{25}=5\).

Answer:

5