Question

question 17. using the pythagorean theorem, determine the distance from point (4, - 3) and the origin. round your answer to the nearest tenth, if necessary

Explanation:

Step1: Identify the coordinates

The origin has coordinates \((0,0)\), and the given point is \((4,-3)\). The horizontal distance \(a = 4 - 0=4\), and the vertical distance \(b=- 3-0=-3\). The Pythagorean theorem for distance \(d\) 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, \(x_1 = 0,y_1 = 0,x_2 = 4,y_2=-3\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 4\) and \(b=-3\) into \(d=\sqrt{a^{2}+b^{2}}\). So \(d=\sqrt{4^{2}+(-3)^{2}}=\sqrt{16 + 9}\).

Step3: Calculate the value

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

Answer:

\(5\)