Question

46 find the distance between (1, 0) and (9, 15). use the distance formula or the pythagorean theorem. distance =

Explanation:

Step1: Identify the coordinates

The two points are \((x_1, y_1) = (1, 0)\) and \((x_2, y_2) = (9, 15)\).

Step2: Calculate the differences

First, find the difference in the x - coordinates: \(x_2 - x_1=9 - 1 = 8\).
Then, find the difference in the y - coordinates: \(y_2 - y_1=15 - 0 = 15\).

Step3: Apply the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute the values we found: \(d=\sqrt{8^2 + 15^2}=\sqrt{64 + 225}=\sqrt{289}\).

Step4: Simplify the square root

Since \(17\times17 = 289\), \(\sqrt{289}=17\).

Answer:

17